This series consists of talks in the area of Quantum Fields and Strings.
For any vertex operator algebra V, Y. Zhu constructed an associative algebra Zhu(V) that captures its representation theory (more generally, given a finite order automorphism g of V, there exists an algebra Zhu_g(V) that captures g-twisted representation theory of V).
We study the defect operator product expansion (OPE) of displacement operators in free and interacting conformal field theories using replica methods. We show that as n approaches 1 a contact term can emerge when the OPE contains defect operators of twist d−2. For interacting theories and general states we give evidence that the only possibility is from the defect operator that becomes the stress tensor in the n→1 limit. This implies that the quantum null energy condition (QNEC) is always saturated for CFTs with a twist gap.
In this talk I will review the state of the art in PN gravity, and in particular its significant advancement via the EFT of spinning gravitating objects. First, I will introduce the concept of a tower of EFTs for the binary inspiral problem. I will then present the intricate formulation of the EFT of spinning objects. Finally, I will present some advanced results accomplished within this framework.
We propose a unified manner of understanding two important phenomena: color confinement in large-N gauge theory, and Bose-Einstein condensation (BEC). We do this by clarifying the relation between the standard criteria, based on the off-diagonal long range order (ODLRO) for the BEC and the Polyakov loop for gauge theory: the constant offset of the distribution of Polyakov line phase is ODLRO.
The elliptic genus is a powerful deformation invariant of 1+1D SQFTs: if it is nonzero, then it protects the SQFT from admitting a deformation to one with spontaneous supersymmetry breaking. I will describe a "secondary" invariant, defined in terms of mock modularity, that goes beyond the elliptic genus, protecting SQFTs with vanishing elliptic genus. The existence of this invariant supports the hypothesis that the space of minimally supersymmetric 1+1D SQFTs provides a geometric model for universal elliptic cohomology. Based on joint works with D. Gaiotto and E. Witten.
In order to satisfy the Reeh-Schlieder theorem, I study the infinite-dimensional Hilbert spaces using von Neumann algebras. I will first present the theorem that the entanglement wedge reconstruction and the equivalence of relative entropies between the boundary and the bulk (JLMS) are exactly identical. Then I will demonstrate the entanglement wedge reconstruction with a tensor network model of von Neumann algebra with type II1 factor, which guarantees the equivalence between the boundary and the bulk.
Subregion duality is an idea in holography which states that every subregion of the boundary theory has a corresponding subregion in the bulk theory, called the 'entanglement wedge', to which it is dual. In the classical limit of the gravity theory, we expect the fields in the entanglement wedge to permit a Hamiltonian description involving a phase space and Poisson brackets. In this talk, I will describe how this phase space arises from the point of view of the boundary theory.
The Monster CFT is a (1+1)d holomorphic CFT with the Monster group global symmetry. The symmetry twisted partition functions exhibit the celebrated Monstrous Moonshine Phenomenon. From a modern point of view, topological defects generalize the notion of global symmetries. We argue that the Monster CFT has a Kramers-Wannier duality defect that is not associated with any global symmetry.
It is a curious numerology that the dynamical scale associated with the instanton of the electroweak SU(2) gauge group is approximately the energy scale of dark energy. We revisit this electroweak quintessence axion scenario, taking into account observational as well as swampland constraints.
Defining entanglement in a continuum field theory is a subtle challenge, because the Hilbert space does not naively factorize into local products.