During the semester we have a high energy seminar and a lunch seminar. In addition to these two seminars we participate in a joint theoretical high energy theory seminar in Newe Shalom. The joint seminar takes place on Tuesdays from 10:30 until 13:30 and includes two talks and lunch. This seminar is attended by the high energy groups of all the Israeli institutions and usually attracts a crowd of roughly twenty participants.
Sun Mon Tue Wed Thu Fri Sat
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.