N4.01

Understanding dynamics of strongly coupled theories is a problem that garners great interest from many fields of physics. In order to better understand theories in 3+1d one can look to lower dimensions for theories which share some properties, but also may exhibit new features that are useful to understand the dynamics. QCD in 1+1d is a strongly coupled theory in the IR, and this talk will explain how to determine if these theories are gapped or gapless in the IR. Moreover, I will describe what IR theory that UV QCD flows to and discuss the IR dynamics. 

There are various aspects of the AdS/CFT correspondence that are rather mysterious. For example, how does the gravitational theory know about a discrete boundary spectrum or how does it know moments of the partition function factorize, given the existence of connected (wormhole) geometries? In this talk I will discuss some recent efforts with Andreas Blommaert and Luca Iliesiu on these two puzzles in two dimensional dilaton gravities. These gravity theories are simple enough that we can understand and propose a resolution to the discreteness and factorization puzzles. I will show that a tiny but universal bilocal spacetime interaction in the bulk is enough to ensure factorization, whereas modifying the dilaton potential with tiny corrections gives a discrete boundary spectrum. We will discuss the meaning of these corrections and how they could be related to resolutions of the same puzzles in higher dimensions. 

In this talk we discuss the set of generalized symmetries associated with the free graviton theory in four dimensions. These are generated by ring-like operators. As for the Maxwell field, we find a set of “electric” and a dual set of “magnetic” topological operators and compute their algebra. The associated electric and magnetic fields satisfy a set of constraints equivalent to the ones of a stress tensor of a 3d CFT. This implies that the generalized symmetry is charged under space-time symmetries, and it provides a bridge between linearized gravity and the tensor gauge theories that have been introduced recently in the context of fractonic systems in condensed matter physics.

Computing Donaldson-Thomas partition function of a G2 manifold has been a long standing problem. The key step for the problem is to understand the G2 instanton moduli space. I will discuss a string theory way to study the G2 instanton moduli space and explain how to compute the instanton partition function for a certain G2 manifold. An important insight comes from the twisted M-theory on the G2 manifold. This talk is based on a work with Michele del Zotto and Yehao Zhou.

In this talk I will review the “holomorphic modular bootstrap,” i.e. the classification of rational conformal field theories via an analysis of the modular differential equations satisfied by their characters. By making use of the representation theory of PSL(2, Zn), we describe a method to classify allowed central charges and weights (c, hi) for theories with any number of characters d. This allows us to avoid various bottlenecks encountered previously in the literature, and leads to a classification of consistent characters up to d = 5 whose modular differential equations are uniquely fixed in terms of (c, hi). In the process, we identify the full set of constraints on the allowed values of the Wronskian index for fixed d ≤ 5.

We discuss the formal relationship between the absence of global symmetries and completeness, both in effective field theory and in quantum gravity. In effective field theory, we must broaden our notion of symmetry to include non-invertible topological operators. However, in gravity, the story is simplified as the result of charged gravitational solitons.

I discuss a novel expansion of superconformal indices of U(N) gauge theories at finite N. When a holographic description is available, the formula expresses the index as a sum over stacks of "giant graviton" branes in the dual string theory. Surprisingly, the expansion turns out to be exact: the sum over strings and branes seems to capture the degeneracy of states expected from saddle geometries such as BPS black holes, while also reproducing the correct degeneracies at lower orders of charges. Based on 2109.02545 with D. Gaiotto.

After a brief review on the classical Prandtl system, we introduce our recent work on the well-posedness and high Reynolds numbers limit for the MHD boundary layer that shows the tangential magnetic field stabilizes the boundary layer. And then we will discuss some instability phenomena of the shear flow for both the classical Prandtl and MHD boundary layer systems. The talk includes some recent joint works with Chengjie Liu, Yaguang Wang on the classical Prandtl equation, and with Chengjie Liu and Feng Xie on the magnetohydrodynamic boundary layer.