Seminars

Title: Some aspects of line defects in d dimensions

Abstract: We consider renormalization group flows on line defects in d dimensions. We define a “defect entropy” and argue that it decreases monotonically during RG flows. We apply this result to line defects which appear in condensed matter and high energy physics, including magnetic (SPT) defects, localized field defects, and Wilson loops. In some of these cases we make some new experimental predictions and in the case of Wilson lines we make some comparisons with localization and holography. 

Title: Automorphic Spectra and the Conformal Bootstrap

Abstract: I will explain that the spectral geometry of hyperbolic manifolds provides a remarkably faithful model of the modern conformal bootstrap. In particular, to each hyperbolic manifold, one can associate a Hilbert space of local operators, which is a unitary representation of a conformal group. The scaling dimensions of the operators are related to the eigenvalues of the Laplacian on the manifold. The operators satisfy an operator product expansion. Finally, one can define their correlation functions and derive bootstrap equations constraining the spectrum. As an application, I will use conformal bootstrap techniques to derive upper bounds on the lowest positive eigenvalue of the Laplacian on closed hyperbolic surfaces and 2-orbifolds. In a number of notable cases, the bounds are nearly saturated by known surfaces and orbifolds. For instance, the bound on all genus-2 surfaces is λ1≤3.8388976481, while the Bolza surface has λ1≈3.838887258. The talk will be based on https://arxiv.org/abs/2111.12716, which is joint work with P. Kravchuk and S. Pal.

Title: Kramers-Wannier-like duality defects in (3+1)d gauge theories

Abstract: I will introduce a class of non-invertible topological defects in (3+1)d gauge theories whose fusion rules are the higher-dimensional analogs of those of the Kramers-Wannier defect in the (1+1)d critical Ising model. As in the lower-dimensional case, the presence of such non-invertible defects implies self-duality under a particular gauging of the discrete (higher-form) symmetries. I will illustrate this by means of the example of SO(3) Yang-Mills (YM) at θ=π,  as well as SU(2)N=4 SYM at τ=i.

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.

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.

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.

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. 

Title: String stars in anti de Sitter space


Abstract: We study the ‘string star’ saddle, also known as the Horowitz-Polchinski solution, in the middle of d+1 dimensional thermal AdS space (d>2). We show that there’s a regime of temperatures in which the saddle is very similar to the flat space solution found by Horowitz and Polchinski. This saddle is hypothetically connected at lower temperatures to the small AdS black hole saddle. We also study, numerically and analytically, how the solutions are changed due to the AdS geometry for higher temperatures. Specifically, we describe how the solution joins with the thermal gas phase, and find the leading correction to the Hagedorn temperature due to the AdS curvature. Finally, we study the thermodynamic instabilities of the solution and argue for a Gregory-Laflamme-like instability whenever extra dimensions are present at the AdS curvature scale.