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Boundaries and Defects in Quantum Field Theory

Conference Date: 
Mardi, Août 6, 2019 (All day) to Vendredi, Août 9, 2019 (All day)
Scientific Areas: 
Condensed Matter
Quantum Information

 

Boundaries and defects play central roles in quantum field theory (QFT) both as means to make contact with nature and as tools to constrain and understand QFT itself. Boundaries in QFT can be used to model impurities and also the finite extent of sample sizes, while interfaces allow for different phases of matter to interact in a controllable way. More formally, these structures shed light on the structure of QFT by providing new examples of dualities and renormalization group flows.  Broadly speaking, this meeting will focus on three areas: 1) formal and applied aspects of boundary and defect conformal field theory, from anomalies and c-theorems to topological insulators, 2) supersymmetry and duality, from exact computations of new observables to the construction of new theories, and 3) QFT in curved space and gravity, from holographic computations of entanglement entropy to ideas in quantum information theory.

Registration for this event is now closed.

  • Natan Andrei, Rutgers University
  • Francesco Benini, SISSA
  • Lorenzo Bianchi, Queen Mary University of London
  • Alejandra Castro, University of Amsterdam
  • Shira Chapman, University of Amsterdam
  • Jaume Gomis, Perimeter Institute
  • Simone Giombi, Princeton University
  • Sergei Gukov, California Institute of Technology
  • Charlotte Kristjansen, Niels Bohr Institute
  • Prem Kumar, Swansea University
  • Edoardo Lauria, Durham University
  • Madalena Lemos, CERN
  • Marco Meineri, EPFL Switzerland
  • Rong-Xin Miao, Sun Yat-Sen University
  • Tatsuma Nishioka, University of Tokyo
  • Natalie Paquette, California Institute of Technology
  • Silvia Penati, University of Milano-Bicocca
  • Leonardo Rastelli, Stony Brook University
  • Shinsei Ryu, University of Chicago
  • Nathan Seiberg, Institute for Advanced Study
  • Arkady Tseytlin, Imperial College London
  • Andrew Baumgartner, University of Washington
  • Alice Bernamonti, Perimeter Institute
  • Gabriel Bilard, University of Cambridge
  • Andreas Blommaert, Ghent University
  • Adam Chalabi, University of Southampton
  • Vitorio A. De Lorenci, Federal University of Itajuba
  • John Estes, New York City College of Technology
  • Federico Galli, Perimeter Institute
  • Lorenzo Di Pietro, Perimeter Institute
  • Danilo Diaz Vazquez, Universidad Andres Bello
  • Bianca Dittrich, Perimeter Institute
  • Laurent Freidel, Perimeter Institute
  • Valentina Forini, City University of London
  • Nicola Gorini, University of Milano
  • Luca Griguolo, University of Parma
  • Himanshu Khanchandani, Princeton University
  • Justin Kulp, Perimeter Institute
  • David Lazowski, Perimeter Institute
  • Ji Hoon Lee, Perimeter Institute
  • Hugo Marrochio, Perimeter Institute
  • Kazunobu Maruyoshi, Seikei University
  • Seyed Faroogh Moosavian, Perimeter Institute
  • Tadashi Okazaki, Perimeter Institute
  • Alexander Patrushev, Bauman Moscow State Technical University
  • Miroslav Rapcak, Perimeter Istitute
  • Caio Cesar Ribeiro, University of Sao Paulo
  • Ronnie Rodgers, University of Southampton
  • Domenico Seminara, University of Florence
  • Barak Shoshany, Perimeter Institute
  • Antonino Travia, University of South Florida
  • Julio Virrueta, Stony Brook Univrsity
  • Ben Webster, Perimeter Institute & University of Waterloo
  • Jingxiang Wu, Perimeter Institute
  • Itamar Yaakov, University of Parma
  • Junya Yagi, Perimeter Institute
  • Lucy Zhang, University of Toronto

Tuesday, August 6th , 2019

Time

Event

Location

9:00 – 9:30am

Registration

Reception

9:30 – 10:15am

Jaume Gomis, Perimeter Institute
Symmetries and Dualities of Abelian TQFTs

Theater

10:15 – 11:00am

Coffee Break

Bistro – 1st Floor

11:00 – 11:45am

Leonardo Rastelli, Stony Brook University
TBD

Theater

11:45 – 12:30pm

Madalena Lemos, CERN
Universality at large transverse spin in defect CFTs

Theater

12:30 – 2:00pm

Lunch

Atrium

2:00 – 2:45pm

Francesco Benini, SISSA
Domain Walls in Super-QCD

Theater

2:45 – 3:30pm

Rong-Xin Miao, Zhongshan University
Weyl Anomaly Induced Current and Holography

Theater

3:30 – 4:15pm

Coffee Break

Bistro – 1st Floor

4:15 – 5:00pm

 Prem Kumar, Swansea University
Wilson line impurities, flows and entanglement entropy

Theater

5:00 – 6:00pm

Wine and Cheese Reception

Reflection Lounge

 

Wednesday, August 7th , 2019

Time

Event

Location

9:30 – 10:15am

Nathan Seiberg, Institute for Advanced Study
Anomalies in the Space of Coupling Constants

Theater

10:15 – 11:00am

Coffee Break

Bistro – 1st Floor

11:00 – 11:45am

Charlotte Kristjansen, Niels Bohr Institute
Integrability of one-point functions in AdS/dCFT with and without supersymmetry

Theater

11:45 – 12:30pm

Sergei Gukov, California Institute of Technology
Algebras of Interfaces

Theater

12:30 – 2:00pm

Lunch

Atrium

2:00 – 2:45pm

Shira Chapman, University of Amsterdam
Complexity for Systems with Defects

Theater

2:45 – 3:30pm

Alejandra Castro, Universiteit van Amsterdam
Wilson lines in AdS3 gravity

Theater

3:30 – 4:15pm

Coffee Break

Bistro – 1st Floor

4:15 –5:00pm

Edoardo Lauria, Durham University
3d Abelian Gauge theories at the Boundary

Theater

 

Thursday, August 8th , 2019

Time

Event

Location

9:30 – 10:15am

Natalie Paquette, California Institute of Technology
Boundaries and Interfaces in 3d, and Applications

Theater

10:15 – 11:00am

Coffee Break

Bistro – 1st Floor

11:00 – 11:45am

Simone Giombi, Princeton University
Wilson loops and defect CFT

Theater

11:45 – 12:30pm

Arkady Tseytlin, Imperial College London
Boundary correlators of Liouville and Toda theories on AdS2 and  AdS/CFT

Theater

12:30 – 2:00pm

Lunch

Atrium

2:00 – 2:45pm

Silvia Penati, University of Milano-Bicocca
BPS Wilson loop in AdS4/CFT3

Theater

2:45 – 3:30pm

Tatsuma Nishioka, University of Tokyo
Entanglement, free energy and C-theorem in DCFT

Theater

3:30 – 4:15pm

Coffee Break

Bistro – 1st Floor

4:15 –5:00pm

Lorenzo Bianchi, Queen Mary University of London
Shape dependence of superconformal defects

Theater

 

Friday, August 9th , 2019

Time

Event

Location

9:30 – 10:15am

Shinsei Ryu, University of Illinois at Urbana-Champaign
Entanglement negativity in many-body systems, and holography

Theater

10:15 – 11:00am

Coffee Break

Bistro – 1st Floor

11:00 – 11:45am

Marco Meineri, École Polytechnique Federale de Lausanne
Colliders and conformal interfaces

Theater

11:45 – 12:30pm

Natan Andrei, Rutgers University
Quantum Work of an Optical Lattice and Boundary Field Theory

Theater

12:30 – 2:00pm

Lunch

Atrium

 

 

Natan Andrei, Rutgers University

Quantum Work of an Optical Lattice and Boundary Field Theory

We study the quantum work associated with the nonequilibrium quench of an optical lattice as it evolves from initial Mott type states with large potential barriers under the Sine-Gordon Hamiltonian that describes the dynamics of the system when the barriers are suddenly lowered.  The calculations are carried out by means of the Boundary Bethe Ansatz approach where the initial and final states of the quench are applied as boundary states on the evolving system. We calculate exactly the Loschmidt amplitude, the fidelity and work distribution characterizing the quenches for different values of the interaction strength.

Francesco Benini, SISSA

Domain Walls in Super-QCD

Four-dimensional Yang-Mills and (massive) QCD with minimal N=1 supersymmetry are theories with multiple gapped vacua. Therefore, different regions of space can sit in different vacua and be connected by BPS domain walls. I will present a compact 3D worldvolume description of the walls, capable of classifying all possible BPS walls between vacua and of capturing a 2nd order phase transition as the quark mass is varied. Such a proposal will be confirmed by explicit 4D constructions of BPS domain walls, extending the existing literature.

Lorenzo Bianchi, Queen Mary University of London

Shape dependence of superconformal defects

The shape deformation of conformal defects is implemented by the displacement operator. In this talk we consider superconformal defects and we provide evidence of a general relation between the two-point function of the displacement and the one-point function of the stress tensor operator. We then discuss the available techniques for the computation of this one-point function. First, we show how it can be related to a deformation of the background geometry. Then we conclude with a discussion of surface defects in four-dimensional N=2 theories, where the chiral algebra provides an additional powerful tool.

Alejandra Castro, University of Amsterdam

Wilson lines in AdS3 gravity

The partnership between 3D gravity and Chern-Simons theory is well-known and powerful, but many aspects of this relation are unclear.
In this talk I'll discuss Wilson lines in Chern-Simons theory and their role in AdS3 gravity. Wilson lines are interesting objects to explore locality in Chern-Simons theory, and how they affect the partnership at the quantum level.

Shira Chapman, University of Amsterdam

Complexity for Systems with Defects

I will start by reviewing the definition and properties of complexity as well as the relevant holographic proposals. I will then describe the results of [1811.12549] where we studied the two holographic complexity proposals for the case of a 2d boundary CFT with a conformal defect using a Randall-Sundrum type model of a thin AdS_2 brane embedded in AdS_3. Our results indicate that this setup can be used to distinguish the two holographic proposals for the complexity. I will also describe results for simple free bosonic field theory models which include two defects on opposite sides of a periodic domain.

Simone Giombi, Princeton University

Wilson loops and defect CFT

I will overview recent results on the defect CFT corresponding to Wilson loop operators in N=4 SYM theory. In particular, I will review the calculation of defect correlators at strong coupling using the AdS2 string worldsheet, and I will present exact results for correlation  functions in a subsector of the defect CFT using localization. I will also discuss a defect RG flow from the BPS to the ordinary Wilson loop,  which can be used to provide a test of the "defect F-theorem" for one-dimensional defects.

Jaume Gomis, Perimeter Institute

Symmetries and Dualities of Abelian TQFTs

Sergei Gukov, California Institute of Technology

Algebras of Interfaces

Prem Kumar, Swansea University

Wilson line impurities, flows and entanglement entropy

Charlotte Kristjansen, Niels Bohr Institute

Integrability of one-point functions in AdS/dCFT with and without supersymmetry

We review recent results on the calculation of one-point functions in dCFTs corresponding to  N=4 SYM with domain walls, discussing supersymmetric as well as non-supersymmetric cases.  In particular, we address the integrability properties of the theories and  the status of  the comparison to dual string theoretical  computations.

Edoardo Lauria, Durham University

3d Abelian Gauge theories at the Boundary

A four-dimensional abelian gauge theory can be coupled to a 3d CFT with a U(1) symmetry living on a boundary. This coupling gives rise to a continuous family of boundary conformal field theories (BCFTs) parametrized by the gauge coupling \tau and by the choice of the CFT in the decoupling limit. Upon performing an Electric-Magnetic duality in the bulk and going to the decoupling limit in the new frame, one finds a different 3d CFT on the boundary, related to the original one by Witten's SL(2, Z) action. In particular the cusps on the real \tau axis correspond to the 3d gauging of the original CFT. We study general properties of this family of BCFTs. We show how to express bulk one and two-point functions, and the hemisphere free-energy, in terms of the two-point functions of the boundary electric and magnetic currents. Finally, upon assuming particle-vortex duality (and its fermionic version), we show how to turn this machinery into a powerful computational tool to study 3d gauge theories.

Madalena Lemos, CERN

Universality at large transverse spin in defect CFTs

We study the spectrum of defect conformal field theories (CFTs), and show the existence of universal accumulation points in the defect spectrum. This is achieved by obtaining an inversion formula for the bulk to defect OPE, akin to the Lorentzian inversion formula of Caron-Huot for CFTs without defects. We conclude by applying the result in examples and with an outlook.

Marco Meineri, École Polytechnique Federale de Lausanne

Colliders and conformal interfaces

We probe a generic two dimensional conformal interface via a collider experiment. We measure the energy and charges which are reflected and transmitted through the interface. If the largest symmetry algebra is Virasoro, the average transmitted energy is independent of the details of the initial state, and is fixed in terms of the central charges and of the two-point function of the displacement operator. The situation is more elaborate when extended symmetries are present. We comment on the bounds imposed by positivity of the total energy flux at infinity, and on applications of the result to the physics of steady states.

Rong-Xin Miao, Zhongshan University

Weyl Anomaly Induced Current and Holography

We show that when an external magnetic field parallel to the boundary is applied, Weyl anomaly give rises to a new anomalous current transport near the boundary. Similar to the Casimir effect, this transport phenomena has its origin in the effect of the boundary on the quantum fluctuations of the vacuum. The near-boundary current takes universal form for general boundary quantum field theories, which are covariant, gauge invariant, unitary and renormalizable. We verify the universal law of current by studying free QFT and holographic BCFT.  Finally, we discuss the so-called "divergence" problem and show that it can be resolved by the law of conservation of charge.

Tatsuma Nishioka, University of Tokyo

Entanglement, free energy and C-theorem in DCFT

The g-theorem is a prominent example of C-theorems in two-dimensional boundary CFT and the extensions are conjectured to hold in higher-dimensional BCFTs. On the other hand, much less is known for C-theorems in a CFT with conformal defects of higher codimensions. I will investigate the entanglement entropy across a sphere and sphere free energy as a candidate for a C-function in DCFT, and show they differ by a universal term proportional to the vev of the stress tensor. Based on this relation, I will propose to use the sphere free energy as a C-function in DCFT. This proposal unifies the previously known theorems and conjectures, and passes several checks, including a few examples in field theories and a holographic proof in simple gravity dual models of DCFTs.

Natalie Paquette, California Institute of Technology

Boundaries and Interfaces in 3d, and Applications

In this talk, I will briefly discuss the construction of semiclassical 1/2-BPS boundary conditions and duality interfaces in 3d N=2 theories, following work with T. Dimofte and D. Gaiotto. Then, I will sketch some mathematical applications of these codimension-1 defects to the geometry of triangulated 4-manifolds and chiral algebras, based on work with T. Dimofte and building off related advances by Gadde, Gukov, and Putrov. I will also mention recent and ongoing work on generating 2d dualities from dual "sandwich" configurations of 3d theories sandwiched by both left and right boundary conditions.

Silvia Penati, University of Milan

BPS Wilson loop in AdS4/CFT3

I will review recent results concerning a general class of parametric BPS Wilson loops in ABJM theory. In particular, I will present a proposal for their exact quantum expression in terms of a parametric Matrix Model and discuss their role in the exact calculation of physical quantities like the Bremsstrahlung function and in testing the AdS4/CFT3 correspondence.

Shinsei Ryu, University of Chicago

Entanglement negativity in many-body systems, and holography

I will discuss entanglement negativity, an entanglement measure for mixed quantum states, in many-body systems, including lattice quantum systems and quantum field theories.
I will also discuss the possible holographic dual description of entanglement negativity in field theories and tensor networks.

Nathan Seiberg, Institute for Advanced Study

Anomalies in the Space of Coupling Constants

We will discuss a new anomaly in the space of coupling constants.  We will demonstrate it and its applications in simple examples and in 4d gauge theories.

Arkady Tseytlin, Imperial College London

Boundary correlators of Liouville and Toda theories on AdS2 and  AdS/CFT

We  observe that boundary correlators of the elementary scalar field of the  Liouville theory defined on rigid  AdS2 background are the same  as the correlators of the chiral stress tensor of the Liouville CFT on the complex plane restricted to the real line. The same relation generalizes to the conformal abelian Toda theory:  correlators of Toda scalars on AdS2 are directly related to those of  the chiral W-symmetry generators in the Toda CFT and thus are essentially controlled by the underlying infinite-dimensional symmetry. These may be viewed as examples of AdS2/CFT1 duality where the CFT1 is the chiral half of a 2d CFT. Similar  relation  applies also to a  non-abelian Toda theory containing a Liouville scalar coupled to a 2d sigma-model originating from the SL(2,R)/U(1) gauged WZW model. Here the Liouville scalar is again dual to the chiral stress tensor T  while the other two scalars are dual to the parafermionic operators V±  of the non-abelian Toda CFT.  The duality  is checked at the next-to-leading order in the large central charge expansion by matching the chiral CFT correlators of (T,V+,V−)  with the boundary correlators of the three Toda scalars given by the tree-level and one-loop Witten diagrams in AdS2. Based on arXiv:1904.12753,1907.01357.

 

Vendredi aoû 09, 2019
Speaker(s): 

We study the quantum work associated with the nonequilibrium quench of an optical lattice as it evolves from initial Mott type states with large potential barriers under the Sine-Gordon Hamiltonian that describes the dynamics of the system when the barriers are suddenly lowered. The calculations are carried out by means of the Boundary Bethe Ansatz approach where the initial and final states of the quench are applied as boundary states on the evolving system.

 

Vendredi aoû 09, 2019
Speaker(s): 

We probe a generic two dimensional conformal interface via a collider experiment. We measure the energy and charges which are reflected and transmitted through the interface. If the largest symmetry algebra is Virasoro, the average transmitted energy is independent of the details of the initial state, and is fixed in terms of the central charges and of the two-point function of the displacement operator. The situation is more elaborate when extended symmetries are present.

 

Vendredi aoû 09, 2019
Speaker(s): 

I will discuss entanglement negativity, an entanglement measure for mixed quantum states, in many-body systems,
including lattice quantum systems and quantum field theories.
I will also discuss the possible holographic dual description of entanglement negativity in field theories and tensor networks.

 

Jeudi aoû 08, 2019
Speaker(s): 

The shape deformation of conformal defects is implemented by the displacement operator. In this talk we consider superconformal defects and we provide evidence of a general relation between the two-point function of the displacement and the one-point function of the stress tensor operator. We then discuss the available techniques for the computation of this one-point function. First, we show how it can be related to a deformation of the background geometry.

 

Jeudi aoû 08, 2019
Speaker(s): 

The g-theorem is a prominent example of C-theorems in two-dimensional boundary CFT and the extensions are conjectured to hold in higher-dimensional BCFTs. On the other hand, much less is known for C-theorems in a CFT with conformal defects of higher codimensions. I will investigate the entanglement entropy across a sphere and sphere free energy as a candidate for a C-function in DCFT, and show they differ by a universal term proportional to the vev of the stress tensor. Based on this relation, I will propose to use the sphere free energy as a C-function in DCFT.

 

Jeudi aoû 08, 2019
Speaker(s): 

I will review recent results concerning a general class of parametric BPS Wilson loops in ABJM theory. In particular, I will present a proposal for their exact quantum expression in terms of a parametric Matrix Model and discuss their role in the exact calculation of physical quantities like the Bremsstrahlung function and in testing the AdS4/CFT3 correspondence.

 

Jeudi aoû 08, 2019
Speaker(s): 

We observe that boundary correlators of the elementary scalar field of the Liouville theory defined on rigid AdS2 background are the same as the correlators of the chiral stress tensor of the Liouville CFT on the complex plane restricted to the real line. The same relation generalizes to the conformal abelian Toda theory: correlators of Toda scalars on AdS2 are directly related to those of the chiral W-symmetry generators in the Toda CFT and thus are essentially controlled by the underlying infinite-dimensional symmetry.

 

Jeudi aoû 08, 2019
Speaker(s): 

I will overview recent results on the defect CFT corresponding to Wilson loop operators in N=4 SYM theory. In particular, I will review the calculation of defect correlators at strong coupling using the AdS2 string worldsheet, and I will present exact results for correlation functions in a subsector of the defect CFT using localization. I will also discuss a defect RG flow from the BPS to the ordinary Wilson loop, which can be used to provide a test of the "defect F-theorem" for one-dimensional defects.

 

Jeudi aoû 08, 2019
Speaker(s): 

In this talk, I will briefly discuss the construction of semiclassical 1/2-BPS boundary conditions and duality interfaces in 3d N=2 theories, following work with T. Dimofte and D. Gaiotto. Then, I will sketch some mathematical applications of these codimension-1 defects to the geometry of triangulated 4-manifolds and chiral algebras, based on work with T. Dimofte and building off related advances by Gadde, Gukov, and Putrov.

 

Mercredi aoû 07, 2019
Speaker(s): 

A four-dimensional abelian gauge theory can be coupled to a 3d CFT with a U(1) symmetry living on a boundary. This coupling gives rise to a continuous family of boundary conformal field theories (BCFTs) parametrized by the gauge coupling \tau and by the choice of the CFT in the decoupling limit. Upon performing an Electric-Magnetic duality in the bulk and going to the decoupling limit in the new frame, one finds a different 3d CFT on the boundary, related to the original one by Witten's SL(2, Z) action.

Pages

Scientific Organizers:

  • Matthew Buican, Queen Mary University of London
  • Davide Gaiotto, Perimeter Institute
  • Christopher Herzog, Stony Brook University & King's College, London
  • Marina Huerta, Centro Atomico Bariloche
  • Kristan Jensen, San Francisco State University
  • Robert Myers, Perimeter Institute
  • Andrew O'Bannon, University of Southampton
  • Brandon Robinson, University of Southampton