Non-integrability in world sheet string theory
In this talk, I would discuss aspects of non-integrability of string world-sheet theories. I will discuss few different cases including black holes and Calabi-Yau cones.
S-Matrix Theory for Massive Higher Spins and the Challenge of UV Completion
Scaling in Quantum Quench : from Holography to Lattices
Systems with time dependent couplings which interpolate between constant values and involve critical points are expected to display universal scaling. Holographic methods have been used to understand some aspects of such quantum quenches, in particular Kibble-Zurek scaling. In the opposite regime of fast quench, holographic methods have uncovered new scaling laws which have been subsequently shown to hold in general continuum quantum field theories. This talk reviews these developments, and explores how these different scaling regimes appear in solvable lattice field systems in one and two space dimensions and relate to other known results for abrupt quenches. I will also discuss possible scaling properties of the entanglement entropy in some one dimensional systems.
Weyl Anomalies and Cosmology
I'll discuss effects of Weyl anomalies arising from renormalization of composite operators in a cosmological context. I’ll first describe a two-dimensional model of gravity in which the nonlocal contributions to the quantum effective action arising from such Weyl anomalies of the cosmological constant operator slow down exponential de Sitter expansion to quasi de Sitter power law expansion and lead to a slow dilution of vacuum energy. I’ll describe methods to systematically compute similar nonlocal effects for general actions in four dimensions for cosmological spacetimes using local renormalization group and compare them with the Barvinsky-Vilkovisky expansion. I’ll conclude by discussing possible implications for primordial magnetogenesis and quantum stability of (anti) de Sitter spacetimes.
Spectral sum rules for conformal field theories in arbitrary dimensions
We derive spectral sum rules in the shear channel for conformal field theories at finite temperature in general d ≥ 3 dimensions. The sum rule states that a weighted integral of the spectral density over frequencies is proportional to the energy density of the theory. We show that the proportionality constant can be written in terms the Hofman-Maldacena variables t_2,t_4 which determine the three point function of the stress tensor. For theories which admit a two derivative gravity dual this proportionality constant is given by d/ 2(d+1). We then use causality constraints and obtain bounds on the sum rule which are valid in any conformal field theory.
Scientific contributions of Spenta Wadia
The Large SpeNta Limit
Michael B Green
Hadronic strings: old and new
A new perspective on holographic entanglement
The by-now classic Ryu-Takayanagi formula associates the entanglement entropy of a spatial region in a holographic field theory with the area of a certain minimal surface in the bulk. As I will explain, despite its simplicity and beauty, this formula raises a number of stubborn conceptual problems. I will present a reformulation that does not involve the areas of surfaces, and that leads to a picture of entanglement in the field theory being carried by Planck-thickness "bit threads" in the bulk. I will argue that this picture helps to resolve a number of the conceptual difficulties surrounding the RT formula.
Growth dynamics and size fluctuations of bacterial cells
Experiments on bacterial cells have revealed many quantitative regularities in their size and compositional dynamics whose origin remains unclear. In a steady environment characterized by constant nutrient concentrations, the size of a single cell grows exponentially with time between birth and division. This is surprising in view of the fact that cell size ultimately depends upon the internal chemical dynamics which is highly nonlinear. The variation of cell size at birth across different cells in the same culture also exhibits unexpected regularities. The talk will briefly describe the phenomena and an attempt to understand them theoretically from mathematical models. In particular it will be argued that mass action chemical dynamics in a class of self-expanding containers possesses a simple mathematical property that results in exponentially growing trajectories being attractors of the dynamics. Further, several features of size fluctuations can be explained by the variation in the first passage time of an internal chemical population reaching a fixed threshold and triggering cell division.
Exotic RG Flows from Holography
Holographic RG flows are studied in an Einstein-dilaton theory with a general potential. The superpotential formalism is utilized in order to characterize and classify all solutions that are associated to asymptotically AdS space-times. Such solutions correspond to holographic RG flows and are characterized by their holographic β-functions. Novel solutions are found that have exotic properties from a RG point-of view. Some have β-functions that are defined patch-wise and lead to flows where the β-function changes sign without the flow stopping. Others describe flows that end in non-neighboring extrema in field space. Finally others describe regular flows between two minima of the potential and correspond holographically to flows driven by the VEV of an irrelevant operator in the UV CFT.
Random Tensor Models and Melonic Large N Limits
On the thermodynamic stability of Black Holes
Among the nonperturbative stability, we examine the possible fragmentation based on the thermodynamic property. The black holes investigated are the rotating AdS black holes as well as those with Gauss-Bonnet term. Unlike black holes in the asymptotic flat spacetime which is stable under fragmentation, we found some parameter region showing the instability under the fragmentation.
Higher Dimensional Field Theories
Quantum field theories in 5,6 dimensional space-time have been extensively studied as they are interesting by their own and also have implied several new features in the theories in 4 or less dimensional space-time. In this talk, we review some features briefly and highlight our recent works.
Issues in Open EFT
Top eigenvalue of a random matrix: Tracy-Widom distribution and third order phase transition
Tracy-Widom distribution describes the probability distribution of the typical fluctuations of the top eigenvalue of a Gaussian (NxN) random matrix. Over the last decade, the same distribution has surfaced in a wide variety of problems from KPZ surface growth, directed polymer, random permutations, all the way to large $N$ gauge theory and wireless communications, with some of these problems having no apriori connection to random matrices. Why is the Tracy-Widom distribution so ubiquitous? In statistical physics, universality is usually accompanied by a phase transition--near a critical point often the details become completely irrelevant. So, is there an underlying phase transition associated with the Tracy-Widom distribution? In this talk, I will demonstrate that for large but finite N, indeed there is an underlying third order phase transition from a `strong' coupling to a `weak' coupling phase--the Tracy-Widom distribution turns out to be the universal crossover function between these two phases for finite but large N. Several examples of this third order phase transition will be discussed.
SYK model, Coadjoint orbits and Liouville bulk dual
We construct coadjoint orbits under 1D reparametrization group (Diff) of AdS$_2$ in terms of explicit metrics. We propose these to be the bulk dual to the low energy configurations of SYK which are also given by Diff-orbits. The coadjoint orbit action is known to be the induced gravity action of Polyakov which is related to Liouville theory. By using this, we compute the low energy action and thermodynamics from the bulk and show that these match those of the SYK model up to identification of parameters.
Free fermions, strings, and the 1/N expansion
One of the leitmotivs in Spenta Wadia’s work has been the interplay between free fermions in low dimension, string theory, and the 1/N expansion. In this talk. I will present some new results along this direction. I will explain how an infinite family of (topological) string theories can be defined at the non-perturbative level in terms of a free Fermi gas in one dimension. I will also discuss some aspects of the 1/N expansion in these systems.
Black Hole dynamics at large D
Cosets and Analogue Monsters in Rational CFT
Some relations between families of RCFTs are explained using a generalised coset construction, and interesting new CFT's are found. This construction yields at least one example of a multi-character CFT analogous to the meromorphic Monster CFT. It is suggested that more may exist.
Fun with K3
I met Spenta 30 years ago, when I came to India to give a set of lectures at a winter school in Kanpur. It was also Ramanujan's centennial, and we watched a TV program on the discovery of his lost notebook by George Andrews. In this talk, I will discuss aspects of string theory on K3, where moch theta functions in Ramanujan's notebook play prominent roles.
The Large N Limit of Chern Simons Vector Models: Past and Present
The large N limit of quantum field theories has always been a topic of great interest to Spenta. One of Spenta’s more recent contributions to this area was to initiate (in collaboration with Simone Giombi, Shiraz Minwalla, myself, Sandip Trivedi and Xi Yin) the study of Chern-Simons theories with vector matter. Much like the ’t Hooft model of 2d QCD, a U(N) Chern-Simons theory coupled to fundamental fermions is effectively a large N vector model, and hence exactly solvable in the large N limit using a variety of techniques. This work has lead to many interesting developments including: a non-supersymmetric bosonization duality (Aharony, Gur-Ari, Yacoby), the realization that a supersymmetric higher-spin gauge theory can arise as a limit of string theory (Cheng, Minwalla, Sharma, and Yin), and new techniques for solving quantum field theories with a slightly-broken higher spin symmetry (Maldacena, Zhiboedov). In this talk we will review some of these developments, and briefly speculate about some unexplored areas that Spenta has encouraged me to look at: bi-fundamental U(N)xU(M) Chern-Simons theories, their holographic duals, and how they might be studied in an M/N expansion.
A holographic view of singularities
The Information Paradox and Complementarity
Disordered metals without quasiparticles, and charged black holes
Experiments in correlated materials have long indicated that it is possible for strongly interacting electrons to form disordered metallics states without quasiparticle excitations or disorder-induced localization. I will describe how a class of SYK models finally provide specific quantum realizations of such states. These modes are also connected, via holography, to charged black holes in anti-de Sitter space.
The story of two $i\epsilon$
Most string theory amplitudes computed using conventional world-sheet method give divergent result. There are two systematic methods for dealing with this problem. One either deforms the integration over the moduli space of Riemann surfaces into complexified moduli space or one represents the amplitudes as sum of Feynman diagrams in string field theory and deforms the integration contour over loop momenta into the complex plane. This talk will discuss the pros and cons of these two approaches and their relationship.
High-dimensional statistics and large-N expansion (OR) One can go only so far from home
I will talk about the relevance of statistical field theory to problems in data science and systems neuroscience.
Conformal bootstrap in Mellin space
I will describe a new formulation of the conformal boostrap which relies on exchange Witten diagrams in Mellin space as the building blocks. In this formalism crossing symmetry is in-built but consistency with the Operator Product Expansion gives rise to new conditions. Using this approach anomalous dimensions and OPE coefficients for the Wilson-Fisher fixed point in 4-epsilon dimension is easily obtained up to O(e^3).
AdS from path-integrals in CFT
Starting from wave functionals in conformal field theories, we would like to explain how we can obtain an Anti de-Sitter space, which may suggest a new interpretation of AdS/CFT, closely related to the tensor network description of AdS/CFT.
Anisotropic Geometries, Viscosity and Cold Atoms
Covariantized M(atrix) Theory
The so-called BFSS M(atrix) theory for D-particles, proposed in 1996, has been the only known workable proposal towards concrete formulation of M theory, whose existence in 11 dimensional space-time is conjectured to be a key feature in still-unknown non-perturbative definitions of string/M theory. However, its formulation has been restricted in a special light-front gauge. Whether and how the M(atrix) theory could be made fully Lorentz covariant in the sense of 11 dimensional Minkowski spacetime has long been one of the important unresolved issues in string/M theory. In this talk, I discuss a possible resolution of this problem on the basis of my recent work.