Seminars

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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. 

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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.

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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.