Seventy-Second Meeting of the North British Mathematical Physics Seminar

Understanding the general form of CFT correlators in momentum space is of interest for a variety of problems including the cosmological bootstrap. In this talk, we review recent work providing a parametric integral representation for the general scalar n-point function. This takes the form of a generalised Feynman integral with the topology of a simplex, featuring an arbitrary function of cross ratios formed from the integration variables. The associated graph polynomials derive from the Laplacian matrix for the simplex, and an inverse parametrisation can be found in terms of the Cayley-Menger matrix. These parametrisations permit the construction of novel weight-shifting operators for CFT correlators, and with further development, could form the starting point for a symmetry-based approach to de Sitter correlators.

According to Wigner's theorem, global symmetries act unitarily (or anti-unitarily) on local observables or states of a quantum system. In this talk, we aim to generalise this statement to the action global symmetries on extended line operators. We propose that the latter transform in (an appropriate notion of) unitary 2-representations of a global symmetry (2-)group, which we classify up to unitary equivalence. Based on arxiv:2411.05067.

After a review of the relevant literature in the (super)conformal bootstrap, we show how new superconformal blocks of short representations beyond half BPS may be computed by means of a supersymmetric generalisation of weight shifting operators, which we define and derive. This approach is valid for any theory whose configuration space is isomorphic to a Grassmannian of \(m|n\) planes in a \(2m|2n\)-dimensional vector space. This includes 4d CFT as well as its \(\mathcal{N}=2,4\) counterparts, among other cases of interest. We briefly discuss some checks, applications to free \(\mathcal{N}=4\) SYM and outlook to other superspaces.

In the absence of dislocations, the hydrodynamics of two-dimensional crystals can be accounted for by considering a set of 1-form global symmetries. In thermal equilibrium, the holographic dual to such a crystal is an AdS black brane charged under 2-form gauge fields [Grozdanov & Poovuttikul, 2018]. By extending the fluid-gravity correspondence to such backgrounds we obtain both dissipative and non-dissipative transport coefficients. We also consider the spectrum of hydrodynamical modes and find instabilities for a certain range of our theory’s parameters. Lastly, we consider the holographic description of momentum relaxation through a closely related bulk dual [Andrade & Withers, 2014] and elaborate on connections between hydrodynamical coefficients in these theories of viscoelasticity and momentum relaxation.

In this talk, I will discuss a new method to extract the effective theory of superfluids with a holographic dual description. This method allows us to derive not only the conventional hydrodynamics far away from the phase transition point but also the equations of Model F of Hohenberg and Halperin, valid in the near critical region. In addition, it provides us with analytic expressions for all the transport and kinetic coefficients, in terms of thermodynamics and black hole horizon data.