Seminars

Title: O(N), Sp(2M), and OSp(1|2M) Models

Abstract: The upper critical dimension of the O(N) vector model is well-known to be 4. In dimension 4-epsilon it is described by the Wilson-Fisher IR fixed point of the O(N) invariant scalar field theory with a small positive quartic coupling. Above 4 dimensions, this theory is non-renormalizable, but in 4+epsilon dimensions it formally has a UV fixed point at small negative coupling. For sufficiently large N, its UV completion in 4<d<6 is the theory of N+1 scalar fields with O(N) invariant cubic interactions. It possesses a weakly coupled IR fixed point in dimension 6-epsilon where the scaling dimensions agree with the 1/N expansion. The scaling dimensions also have imaginary parts that are exponentially small in N; this suggests the existence of near-critical behavior in 5 dimensions. 

Replacing N of the scalar fields by 2M anticommuting scalars, we find Sp(2M) invariant fixed points with imaginary coupling constants in dimension 6-epsilon. In the special case M=1 the symmetry is enhanced to OSp(1|2), and we argue that this theory describes the critical behavior of the zero-state Potts model, or equivalently the random spanning forests. We end by discussing the OSp(1|4) invariant fixed point of the field theory with quintic interactions. Its upper critical dimension is 10/3, and the 10/3-epsilon expansion provides estimates of new critical exponents in d=3.    

Title: A new look at completeness and generalized symmetries

Abstract: We describe a proposal for completeness in QFT. It asserts that the physical observable algebras produced by local degrees of freedom are the maximal ones compatible with causality. We elaborate on equivalent statements to this idea such as the non-existence of generalized symmetries and the uniqueness of the net of algebras. For non-complete theories, we explain how the existence of generalized symmetries is unavoidable, and further, that they always come in dual pairs with precisely the same size”, measured by an algebraic index. Entropic order/disorder parameters can be defined that sense the dual pairs of generalized symmetries and satisfy a “certainty relation”. We briefly describe applications to understand the density of charged states and to holography.

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Title: Exactly Marginal Deformations and their Supergravity Duals


Abstract: We study the space of supersymmetric AdS5 solutions of type IIB supergravity corresponding to the conformal manifold of the dual N = 1 conformal field theories. We show that the background geometry naturally encodes a generalised holomorphic structure, dual to the superpotential of the field theory, with the existence of the full solution following from a continuity argument. In particular, we address the long-standing problem of finding the gravity dual of the generic N = 1 deformations of N = 4 super Yang-Mills: though we are not able to give it in a fully explicit form, we provide a proof-of-existence of the supergravity solution. Using this formalism, we derive a new result for the Hilbert series of the deformed field theories.

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Title: Complexity=Anything?


Abstract: Motivated by holographic complexity, we examine a new class of gravitational observables in asymptotically AdS space associated with codimension-one slices or with codimension-zero regions.  We argue that any of these observables is an equally viable candidate as the extremal volume for a gravitational dual of complexity.

Title: Static Responses and Symmetries of Black Holes

Abstract: I will discuss features of the static responses of black holes in General Relativity. In particular, I will describe how black hole static responses are defined in point particle effective theory and will explain how the vanishing of black hole Love numbers is a consequence of symmetries of the wave equation in black hole backgrounds.

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Title: Line Operators in Chern-Simons-Matter Theories and Bosonization in Three Dimensions


Abstract: We study Chern-Simons theories at large N with either bosonic or fermionic matter in the fundamental representation. The most fundamental operators in these theories are mesonic line operators, the simplest example being Wilson lines ending on fundamentals. We classify the conformal line operators along an arbitrary smooth path as well as the spectrum of conformal dimensions and transverse spins of their boundary operators at finite ‘t Hooft coupling. These line operators are shown to satisfy first-order chiral evolution equations, in which a smooth variation of the path is given by a factorized product of two line operators. We argue that this equation together with the spectrum of boundary operators are sufficient to uniquely determine the expectation values of these operators. We demonstrate this by bootstrapping the two-point function of the displacement operator on a straight line. We show that the line operators in the theory of bosons and the theory of fermions satisfy the same evolution equation and have the same spectrum of boundary operators.