Tag - Gauge theory

Zohreh Davoudi: Quantum simulating hadronic scattering: From confining spin models to gauge theories

1st March, 2024

An exciting promise of quantum simulators is to enable a first-principles look into the real-time dynamics of matter after high-energy collisions of hadrons and nuclei, which mimic conditions in the early universe. To realize such a promise, first the gauge theories of the Standard Model should be mapped to quantum simulators. Then complex initial states, in the form of moving wave packets of composite (bound) states of elementary constituents, need to be prepared. While much progress has happened in the former in recent years, developments in the latter are just starting to gain momentum. In this talk, I will provide three examples from our recent work to demonstrate concrete proposals and algorithms for hadronic wave-packet preparations in confining models, from Ising spin systems to the low-dimensional abelian lattice gauge theories. These examples involve a range of platforms, from (solid-state and atomic) analogue quantum simulators to digital quantum computers. I will further present results for numerical studies of expected scattering outcomes, and conditions for observing inelastic channels, along with a demonstration of a high-fidelity meson wave packet generated on a trapped-ion quantum computer.

Silvia Nagy: From gauge theory to gravity on curved backgrounds

24th January, 2024

The double copy programme aims to construct gravitational quantities from suitably defined "products" of analogous quantities in gauge theory. It was initially developed in the context of scattering amplitudes and hence appears biased towards perturbation theory in flat backgrounds. I will give an overview of recent efforts to extend the double copy beyond flat spacetimes, and comment on possible connections to cosmology and holography.

Anton Ilderton: Strong-field and non-perturbative amplitudes

22nd January, 2024

A linear code is a vector subspace of đť”˝qn, where đť”˝q is a finite field with q elements. The family of linear error-correcting codes are specially important when one is attempting to transmit messages across a noisy communication channel. Data can be corrupted in transmission or storage by a variety of undesirable phenomenon, such as radio interference, electrical noise, scratch, etc.. It is useful to have a way to detect and correct such data corruption. An error-correcting code can correct more errors larger is its minimum distance. This course aims to introduce a family of error-correcting codes, the Algebraic Geometry Codes, and show how to use the theory of semigroups to improve the minimum distance of the code. This construction of codes make use of a function field in one variable over a finite field. We will show how the local information in one or two rational places, the knowledge of the semigroup in these places, can be used to improve the minimum distance of the code.

Ben Webster: Finite W-algebras as Coulomb branches

29th August, 2023

I'll discuss how we can understand finite W-algebras of type A as Coulomb branches of quiver gauge theories, and the insights this gives us on their representation theory and geometry. If I have time, I may also engage in some irresponsible speculation about the BCD case.

Antonio Duarte Pereira: Fixing the gauge-fixing procedure: a non-perturbative concern

16th June, 2023

The treatment of gauge theories in the continuum typically requires the introduction of a gauge-fixing condition. In perturbation theory, the ingenious Faddeev-Popov trick is widely used allowing for the explicit evaluation of gauge fields propagators. However, in stronglycoupled regimes, the assumptions behind the Faddeev-Popov construction do not hold. Gauge fields that fulfil the gauge condition and are connected by gauge transformations are still present in the configuration space - they are the so-called Gribov copies. In this talk, I will present an overview of the problem together with recent developments on how to deal with gauge copies in practice. Most of the presentation will be focused on Yang-Mills theories, but comments that are relevant for the quantum-field theoretic formulation of quantum gravity will be made whenever possible.

Ilya Chevyrev: Invariant measure and universality of the 2D Yang-Mills Langevin dynamic, II

13th June, 2023

In this talk, I will present a recent work on the invariance of the 2D Yang-Mills measure for its Langevin dynamic. The Langevin dynamic both in 2D and 3D had previously been constructed in joint work with Chandra-Hairer-Shen, but it was an open problem to show the existence of an invariant measure even in 2D. In establishing this invariance, we follow Bourgain’s invariant measure argument by taking lattice approximations, but with several twists. An important one, which I will focus on, is that the approximating invariant measures require gauge-fixing, which we achieve by developing a rough version of Uhlenbeck compactness combined with rough path estimates of random walks. I will also present several corollaries of our main result, including a representation of the YM measure as a perturbation of the Gaussian free field, and a new universality result for its discrete approximations.

Hao Shen: Invariant measure and universality of the 2D Yang-Mills Langevin dynamic, I

13th June, 2023

In an earlier work with Chandra, Chevyrev and Hairer, we constructed the local solution to the stochastic Yang-Mills equation on 2D torus, which was shown to have gauge covariance property and thus induces a Markov process on a singular space of gauge equivalent classes. In this talk, we discuss a more recent work with Chevyrev, where we consider the Langevin dynamics of a large class of lattice gauge theories on 2D torus, and prove that these discrete dynamics all converge to the same limiting dynamic. A novel step in the argument is a geometric way to identify the limit using Wilson loops. This universality of the dynamics is crucial for obtaining a sequence of important results for 2D Yang-Mills, including for instance the invariance of the 2D Yang-Mills measure for its Langevin dynamic, which will be discussed by Ilya Chevyrev.

Yuya Murakami: A proof of a conjecture by Gukov-Pei-Putrov-Vafa

9th March, 2023

In 2020, Gukov-Pei-Putrov-Vafa conjectured that Witten-Reshetikhin-Turaev (WRT) invariants are radial limits of homological blocks, which are q-series introduced by them for plumbed 3-manifolds with negative definite linking matrices. In this talk, I prove their
conjecture with three key ideas: (1) To develop a new asymptotic formula by the Euler-Maclaurin summation formula. Then, we can compare asymptotic expansions of WRT invariants and homological blocks; (2) To prove that the conjecture is deduced from the holomorphy of a rational function defined by adding parameters for an expression of WRT invariants; (3) To prove the holomorphy by the induction on pruning of a plumbing graph.

Rajesh Gopkumar: Deriving Gauge-String Duality

1st February, 2022

Gauge (or Yang-Mills) theories are the building blocks of our current physical understanding of the universe. In parallel, string theory is a framework for a consistent quantum description of gravity. Gauge-String duality a.k.a. the AdS/CFT correspondence is a remarkable connection between these two very different classes of theories. This has, in fact, been one of the main engines driving progress in theoretical physics over the last two decades. I will begin by discussing why it is important to arrive at a first principles understanding of the underlying mechanism of this duality relating quantum field theories and string theories (or other theories of gravity). I will then proceed to discuss a very general approach which aims to relate large N QFTs and string theories, starting from free field theories. This corresponds to a tensionless limit of the dual string theory on AdS spacetime. Finally, I will discuss specific cases of this limit for AdS3/CFT2 and AdS5/CFT4, where one has begun to carry this programme through to fruition, going from the string theory to the field theory and vice versa.

Roberta Iseppi: The BV-BRST cohomology for U(n)-gauge theories induced by finite spectral triples

17th August, 2021

The Batalin–Vilkovisky (BV) formalism provides a cohomological approach for the study of gauge symmetries: given a gauge theory, by introducing extra (non-existing) fields, we can associate to it two cohomology complexes, the BV and the BRST complex. The relevance of these complexes lies in the fact that their cohomology groups capture interesting physical information on the initial theory. In this talk we describe how both these complexes can be seen as Hochschild complexes of a graded algebra B over a bimodule M. By focusing on U(n)-gauge theories induced by a finite spectral triple on Mn(ℂ), we explain how the pair (B,M) is naturally encoded, respectively, in the BV spectral triple associated to the theory for the BV complex and in its gauge - fixed version for the BRST one. This result further reinforces the idea that the BV construction naturally inserts in the framework provided by non-commutative geometry.