High Energy Physics

1. The notion of wall-crossing structure (as defined by Maxim Kontsevich and myself in arXiv: 1303.3253)
provides the  universal framework for description of different types of wall-crossing formulas (e.g. Cecotti-Vafa in 2d or KSWCF in 4d). It also gives
a language and tools for proving algebraicity and analyticity of arising generating series (e.g. for BPS invariants).

2. Holomorphic Floer theory is the Floer theory of a pair of complex Lagrangian subvarieties  of a complex symplectic manifold (maybe infinite-dimensional).
This geometry underlies several important topics, both in mathematics and physics. Those  include  questions about analytic continuation of exponential integrals
(e.g. Feynman integrals),
deformation quantization of holomorphic symplectic manifolds (and related Riemann-Hilbert correspondences), Geometric Langlands correspondence, etc.

3. It was known for a long time that many a priori divergent series (like e.g. formal WKB series for solutions of equations with a small parameter) become analytic or meromorphic functions after taking their Laplace transform
(Borel resummation). This property was called  the resurgence property of the divergent series. The relation of the resurgence phenomenon to simplest wall-crossing formulas was realized in the early 90's in the work of French mathematicians (Ecale, Voros, Pham , Malgrange and  others).

I plan to discuss how the combination of 1 and 2 can be applied to 3 in a very general situation.
Main idea goes back to our theory of Donaldson-Thomas invariants (arXiv: 0811.2435).
Namely, analyticity of the formal series  follows from existence of a global analytic object which is glued from the local ones by means of the formal series.
This analytification of  an a priori formal variety is a by-product of the growth estimates on the data of the underlying wall-crossing structure.

In case of the Holomorphic Floer theory (which underlies e.g. the Stokes phenomenon for the WKB solutions of PDE or difference equations) one needs an estimate on the number of pseudo-holomorphic discs
with the boundary on the union of our Lagrangian subvarieties. In practice it often appears as an estimate on the number of gradient lines between two critical points
of the action or potential.

The past few years have seen a surge of interest in six-dimensional superconformal field theories (6D SCFTs).  Notably, 6D SCFTs have recently been classified using F-theory, which relates these theories to elliptically-fibered Calabi-Yau manifolds.  Classes of 6D SCFTs have remarkable connections to structures in group theory and therefore provide a physical link between two seemingly-unrelated mathematical objects.  In this talk, we describe this link and speculate on its implications for future studies of 6D SCFTs.

3d N=4 theories on the sphere have interesting supersymmetric sectors described by 1d QFTs and defined as the cohomology of a certain supercharge. One can define such a 1d sector for the Higgs branch or for the Coulomb branch. We study the Higgs branch case, meaning that the 1d QFT captures exact correlation functions of the Higgs branch operators of the 3d theory. The OPE of the 1d theory gives a star-product on the Higgs branch which encodes the data of these correlation functions. When the 3d theory is superconformal, the 1d theory is topological and coincides with the known construction in flat space, where the topological 1d theory lives in the cohomology of Q+S. Our construction thus generalizes it away from the conformal point. We then focus on theories constructed from vector and hypermultiplets. Using supersymmetric localization, we explicitly describe their 1d sector as the gauged topological quantum mechanics, or equivalently a gaussian theory coupled to a matrix model. This provides a very simple technique to compute the Higgs branch correlators.

The Sachdev-Ye-Kitaev model exhibits conformal invariance and a maximal Lyapunov exponent in the large-N and low temperature limit, and thus belongs to the same universality class as a two-dimensional anti-de Sitter black hole. Poles corresponding to a tower of operators that are bilinear in the microscopic Majorana fermions can be found in the four-point function of the fermions. We propose a renormalization theory for UV perturbations to the model, and derive an effective action for the soft mode of the model that results from integrating out the lowest resonance and which is dominant in the IR. We show that a two-dimensional dilaton theory with a quadratic term precisely reproduces this effective action on its boundary.

We will study the entanglement structure of states in Chern-Simons (CS) theory defined on n-copies of a torus. We will focus on states created by performing the path-integral of CS theory on special 3-manifolds, namely link complements of n-component links in S^3. The corresponding entanglement entropies provide new framing independent link-invariants. In U(1)_k CS theory, we will give a general formula for the entanglement entropy across a bi-partition of a generic n-link into sub-links. In the non-Abelian case, we study various interesting 2 & 3-links including the Whitehead link & Borromean rings, both of which have non-trivial entanglement entropies. 

In this talk, we explore the possibility of gravitational wave production due to ultra-relativistic bubble wall collisions. This occurs due to a process of post-inflationary vacuum decay that takes place via quantum tunnelling within a warped throat (of Randall-Sundrum type). We emphasise the differences between vacuum decay via quantum tunnelling, and a thermal first order phase transition, and how potential gravitational wave signals from both processes differ. We explore a specific example in the context of type IIB string theory, although we argue that our conclusions are more generally applicable to theories with hidden sectors featuring metastable vacua. Many such transitions could have occurred in the post-inflationary Universe, as a large number of throats with exponentially different IR scales can be present in the string landscape, potentially leading to several signals of widely different frequencies – a soundscape connected to the landscape of vacua. Future detectors like LISA will have the required sensitivity to detect these potential signals.

I will discuss the coupling of non-relativistic field theories to curved spacetime, and develop a framework for analyzing the possible structure of non-relativistic (Lifshitz) scale anomalies using a cohomological formulation of the Wess-Zumino consistency condition. I will compare between cases with or without Galilean boost symmetry, and between cases with or without an equal time foliation of spacetime. In 2+1 dimensions with a dynamical critical exponent of z=2, the absence of a foliation structure allows for an A-type anomaly in the Galilean case, but also introduces the possibility of an infinite set of B-type anomalies.

I will also derive Ward identities for flat space correlation functions in Lifshitz field theories, and develop a method for calculating Lifshitz anomaly coefficients from these correlation functions using split dimensional regularization.

Two-dimensional materials such as graphene sheets can serve as excellent detectors for dark matter (DM) with couplings to electrons. The ionization energy of graphene is O(eV), making it sensitive to DM as light as an MeV, and the ejected electron may be detected without rescattering in the target, preserving directional information. I will describe the first experimental proposal for directional detection of MeV-GeV scale DM, which can be implemented in the PTOLEMY relic neutrino experiment and has comparable sensitivity to proposals using semiconductor targets. I will also describe some potential avenues for using gapless systems like Weyl semimetals to detect DM down to the keV limit for warm DM.

When the wavefunction of a macroscopic system unitarily evolves from a low-entropy initial state, there is good circumstantial evidence it develops "branches", i.e., a decomposition into orthogonal components that can't be distinguished from the corresponding incoherent mixture by feasible observations, with each component a simultaneous eigenstate of preferred macroscopic observables.  Is this decomposition unique?  Can the number of branches decrease in time?

Answering these questions is hard because branches are defined only intuitively, much like early investigations of algorithms prior to the Church–Turing thesis.  A rigorous definition could give a speed up to certain non-stationary matrix-product state numerical simulations, as well as solve Kent's Set Selection problem in the consistent histories formalism, a 20-year-old open challenge in the foundations of quantum mechanics. I introduce some tentative definitions based on the idea of redundant information, and establishing a uniqueness theorems. A key counterexample is provided by the Shor error-correction code, which demonstrates that branch structure with robust, redundant records on macroscopic scales can hide incompatible (noncommuting) structure on microscopic scales.

We study the effective twisted superpotential of 3d N=2 gauge theories compactified on a circle.  This is a rich object which encodes much of the protected information in these theories.  We review its properties, and survey some applications, including the algebra of Wilson loops, computation of supersymmetric partition functions on S^1 bundles, and the reduction of 3d dualities to two dimensions.

We introduce a simple and modern discussion of rotational superradiance based on quantum field theory. We work with an effective theory valid at scales much larger than the size of the spinning object responsible for superradiance. Within this framework, the probability of absorption by an object at rest completely determines the superradiant amplification rate when that same object is spinning. We first discuss in detail superradiant scattering of spin 0 particles with orbital angular momentum l = 1, and then extend our analysis to higher values of orbital angular momentum and spin. Along the way, we provide a simple derivation of vacuum friction—a “quantum torque” acting on spinning objects in empty space. Our results apply not only to black holes but to arbitrary spinning objects. We also discuss superradiant instability due to formation of bound states and, as an illustration, we calculate the instability rate Γ for bound states with massive spin 1 particles.