This series consists of talks in the area of Quantum Fields and Strings.
String theory provides us with 8d supersymmetric gauge theories with gauge algebras su(N), so(2N), sp(N), e_6, e_7 and e_8, but no construction for so(2N+1), f_4 and g_2 is known. If string theory is universal in 8 dimensions, this pattern requires explanation. I will show that the theories for f_4 and so(2N+1) have a global gauge anomaly in flat space, while g_2 does not have it. Surprisingly, we also find that the sp(N) theories, arising from example from O7^+ planes in string theory, have a subtler gauge anomaly.
We study the spectrum of local operators living on a defect in a generic conformal field theory, and their coupling to the local bulk operators. We establish the existence of universal accumulation points in the spectrum at large s, s being the charge of the operators under rotations in the space transverse to the defect. Our tools include a formula that inverts the bulk to defect OPE and is analytic in s, analogous to the Caron-Huot formula for the four-point function. Some important assumptions are made in deriving this result: we comment on them.
Topological defect operators are extended operators in a quantum field theory (QFT) whose correlation functions are independent of continuous changes of the ambient space. They satisfy nontrivial fusion relations and put nontrivial constraints on the QFT itself and its deformations (such as renormalization group (RG) flows). Canonical examples of topological defect operators include generators of (higher-form) global symmetries whose constraints on the QFT have been well-studied.
States of a CFT's subregions are consistent with a given global state. For a holographic CFT, this amounts to different entanglement wedges being patches of the same geometry. What relations between them make this possible?
I derive a universal upper bound on the capacity of any communication channel between two distant systems. The Holevo quantity, and hence the mutual information, is at most of order EΔt/ℏ, where E the average energy of the signal, and Δt is the amount of time for which detectors operate. The bound does not depend on the size or mass of the emitting and receiving systems, nor on the nature of the signal. No restrictions on preparing and processing the signal are imposed.
We study the conjectured holographic duality between entanglement of purification and the entanglement wedge cross-section. We generalize both quantities and prove several information theoretic inequalities involving them. These include upper bounds on conditional mutual information and tripartite information, as well as a lower bound for tripartite information. These inequalities are proven both holographically and for general quantum states.
All physical constraints of the conformal bootstrap in principle arise by applying linear functionals to the conformal bootstrap equation. An important goal of the bootstrap program is to identify a suitable basis for the space of functionals -- one that would allow us to solve crossing analytically. In my talk, I will describe two particularly convenient choices of the basis for the 1D conformal bootstrap. The two bases manifest the crossing symmetry of the four-point function of a generalized free boson and generalized free fermion respectively.
We consider planar hairy black holes in five dimensions with a real scalar field in the Breitenlohner-Freedman window and show that is possible to derive a universal formula for the holographic speed of sound for any mixed boundary conditions of the scalar field. As an example, we locally construct the most general class of planar black holes coupled to a single scalar field in the consistent truncation of type IIB supergravity that preserves the SO(3)xSO(3) R-symmetry group of the gauge theory.
I will discuss constraints on the S-matrix of gapped, Lorentz invariant quantum field theories due to crossing symmetry, analyticity and unitarity. In particular I will bound cubic couplings, quartic couplings and scattering lengths relevant for the elastic scattering amplitude of two identical scalar particles. After a warm-up in 1+1 dimensions I will move to 3+1 dimensions. In the cases where the results can be compared with results in the older S-matrix literature they are in excellent agreement.
We derive constraints on the operator product expansion of two stress tensors in conformal field theories (CFTs). In large N CFTs with a large gap to single-trace higher spin operators, we show that the coupling of two stress tensors to other single-trace operators ("TTO") is suppressed by powers of the higher spin gap, dual to the mass scale of higher spin particles in AdS. The absence of light higher spin particles is thus a necessary condition for the existence of a consistent truncation to general relativity in AdS.