Arrival & coffee

Numerical experiments on coefficients of instanton partition functions 

Aradhita Chattopadhyaya  (Dublin Institute for Advanced Studies)

We analyze the coefficients of partition functions of Vafa-Witten theory for the complex projective plane. We experimentally study the growth of the coefficients for gauge group SU(2) and SU(3), which are examples of mock modular forms of depth 1 and 2 respectively. We also introduce the notion of "mock cusp form, and study an example of weight 3 related to the SU(3) partition function. Numerical experiments on the first 200 coefficients suggest that the coefficients of a mock modular form of weight k grow as the coefficients of a modular form of weight k, that is to say as n^(k−1). On the other hand the coefficients of the mock cusp form appear to grow as n^(3/2), which exceeds the growth of classical cusp forms of weight 3. We provide bounds using saddle point analysis, which however largely exceed the experimental observation.

Matrix Entanglement 

Vaibhav Gautam (University of Surrey)

In gauge/gravity duality, matrix degrees of freedom on the gauge theory side play important role for the emergent geometry. In this paper, we discuss how the entanglement on the gravity side can be described as the entanglement between matrix degrees of freedom in the dual gauge theory. We consider several classes of quantum states to which our approach can be crucial. When applied to fuzzy sphere, matrix entanglement can be used to define the usual spatial entanglement in two-brane or five-brane world-volume theory nonperturbatively in a regularized setup. Another application is to a small black hole in AdS_5 X S^5 that can evaporate without being attached to a heat bath, for which our approach suggests a gauge theory origin of the Page curve. The confined degrees of freedom in the partially-deconfined states play a crucial role in recovery of the Page curve.

Lunch

Lessons from self-dual gravity 

Ricardo Monteiro (Queen Mary University of London)

We will discuss how important problems in general relativity have a solvable counterpart in self-dual gravity. This theory is not only a toy model, but constitutes a particular (integrable) sector of general relativity, shedding light on its perturbative structure, celestial formulation and quantum dynamics.

Entanglement Entropy via replica trick and theories with islands in d dimensional static backgrounds 

Arvind Shekar (University of Southampton)

The study of entropy and entanglement entropy (EE) in field theories along with gravity has been fruitful in uncovering the inconsistencies within our theories, such as the information paradox, and has also provided us with a direction to resolve them. Studies of EE and its quantum corrections, has led to a recent (2019) proposal called islands that possibly resolves the information paradox in two-dimensional gravity. Are there islands when one considers a similar prescription for the EE in higher dimensions (d>2)? To explore this would require to know the EE for a QFT state in a region in higher dimensional black hole backgrounds (which has not been explored). We will see how to calculate this using the replica trick in a region on a static black hole background in general dimensions. We will then motivate how this can be used to obtain constraints on a QFT living on a black hole background in general dimensions if it must yield islands and solve the paradox.  

Tea & coffee

Comments on BPS Observables and Gravity from Matrix Models 

Alan Rios Fukelman (King's College)

In this talk, I will review some recent developments in the study of matrix models in the large N limit and how it allows us to characterize the perturbative regime of a general class of such models containing a potential with infinite single and double trace deformations. I will then review how these results allow us to obtain exact results for BPS observables in certain N=2 Lagrangian Super Conformal Field Theories and discuss the implications for the 2- and 3-point functions of Chiral Primary Operators of arbitrary scaling dimensions in these theories. I will also comment on the application of these tools to the study of lower-dimensional theories of gravity and discuss some open problems for which Matrix Model techniques can provide insight.