In this talk I discuss Hamiltonian truncation, a toolkit to construct quantum field theories. Hamiltonian truncation is in many ways orthogonal to the more familiar lattice regularization, and it can be used to systematically compute QFT observables with little computational effort. In the first part of this talk I will review the basic ideas…

In this talk, I will explain how to understand the symplectic structure of the gravitational phase space in AdS in terms of the quantum overlap in the holographically dual CFT. As an application, I will use this to study the boundary description of the volume of maximal Cauchy slices. I will construct the boundary deformation that is conjugate…

We study the quantum mechanics of 3-index Majorana fermions $\psi^{abc}$ governed by a quartic Hamiltonian with $O(N)^3$ symmetry. Similarly to the Sachdev-Ye-Kitaev model, this tensor model has a solvable large $N$ limit dominated by the melonic diagrams. For $N=4$ the total number of states is $2^{32}$, but they naturally break up into…

* Please note the special time and room. *

I will present a status report for the study of confining strings. First, I will focus on confining strings in massive adjoint two-dimensional QCD, where analytical progress is most straightforward to achieve. Then I will describe lessons learnt from this exercise for confining strings in…

In a TQFT of homological type, such as arises from the topological twist of a supersymmetric theory, it is well known that the local operators form an algebra, associative in dimension d >= 1 and commutative in d >= 2. The product comes from collision of operators. I will explain how modern mathematical ideas in TQFT (in particular, the…

We study the phase diagram of SU(N)XSU(N) gauge theory with massive bifundamental Fermion at zero temperature. Assuming that the theory is confining and gapped, some constraints that come from anomalies can be put on the phase diagram as a function of the two theta- angles. We combine these constraints with computations that are valid in the…

Over the past two decades, Vertex Operator Algebras (VOA) have appeared in various contexts in gauge theory. I will discuss a class of VOAs arising as algebras of local operators at junctions of interfaces in four-dimensional N=4 super Yang-Mills theory. The simplest trivalent junction leads to a three-parameter family of algebras $Y_{L,M,N}$…

In this talk I will discuss how to apply the S-matrix bootstrap maximization program to the 2d bosonic O(N) integrable model which has N species of scalar particles with mass m and no bound states. We show that the known S-matrix follows from maximizing a linear functional in the space of S-matrices allowed by the analyticity, unitarity, and…

After a review of a novel low energy effective action for the Schwinger-Keldysh generating function, I will describe how it captures information on the entropy current, Onsager relations, and new constraints on transport.

We show that exact results (at all energy scales) can be obtained in double-scaled SYK, which is the usual SYK model with the number of fermions in the interaction scaling as \sqrt{N}. These include the calculation of the full four-point function. The analysis does not involve summations of Feynman diagrams, but rather uses combinatorial tools…

The two-point functions <O^n(x) Obar^n(y)> for generator O of Coulomb branch chiral rings in D=4 N=2 SCFT will be determined universally to all orders in 1/n by the theory's a-anomaly.

The calculation will be done using the method of large-charge expansion presented in [1706.05743]; the absence of F-terms in the (R-charge)^(-1)…

It is important to understand the origin of exceptional symmetries like E7 duality in 4d M-Sugra. Depending on the context and the defining property at work (anomaly or divergence cancellation, attractor mechanism, classification of supergauge theories in 4, 5 or 6d, 2d integrable systems...) the En groups appear in various families. Cross…

I will describe recent progress on the study of solvable irrelevant deformations of two dimensional conformal field theories, focusing on the torus partition sum of these theories. I will also discuss some related solvable irrelevant deformations of string theory on AdS_3.

A new class of higher-spin gauge theories associated with various Coxeter groups is proposed. The emphasize is on the $B_p$--models. The multi-particle $B_2$--higher-spin theory is conjectured to be associated with String Theory. $B_p$--higher-spin models with $p>2$ are anticipated to be dual to the rank-$p$ boundary tensor sigma-models. $B…

**Abstract: **Borcherds Kac-Moody (BKM) algebras are a generalization of familiar Kac-Moody algebras with imaginary simple roots. On the one hand, they were invented by Borcherds in his proof of the monstrous moonshine conjectures and have many interesting connections to new moonshines, number theory…

Eigenstate thermalization hypothesis (ETH) is a phenomena often observed in systems characterized by quantum chaos. In this talk, we study ETH in 2d CFTs with large central charges. In particular, we focus on observables consisting of bilocal "probe" operators $\mathcal{O}_L(x)\mathcal{O}_L(0)$. A sharp feature of ETH in this context is the so…

In this talk I review new results obtained for SCFT's in 4 and 5 dimensions by compactifying 6 dimensional (1,0) SCFT's on a circle or on Riemann surfaces.

After recalling how some 4d N=2 gauge theories arise from reductions of 6d N=(2,0) superconformal theories on a Riemann surface, I will discuss two discrete quotients with codimension 2 orbifold singularities. In the first case the orbifold acts by rotations around one plane of the 4d N=2 theory; this is related to a Gukov-Witten surface…

In this talk we will review some results and conjectures about non-supersymmetric bifundamental $U(N)\timesU(M)$ Chern-Simons coupled to matter. It is an apparently unique feature of three-dimensions that one can easily define a variety of non-supersymmetric lines of conformal fixed points via the Chern-Simons kinetic term for a gauge field. An…

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