High Energy Physics Theory

We study the effects of addition of Chern-Simons(CS) term in the minimal Yang Mills(YM) matrix model composed of two2?2matrices withSU(2)gauge andSO(2)global symmetry. We obtain the Hamiltonian of this system in appropriate coordinates and demonstrate that its dynamics is sensitive to the values of both the CS coupling,κ, and the conserved conjugate momentum,p?, associated toSO(2)symmetry. We examine the behavior of the emerging chaotic dynamics by computing the Lyapunov exponents and plotting the Poincaré sections as these two parameters are varied and, in particular, find that the largest Lyapunov exponents evaluated within a range of values ofκare above that is computed atκ=0, forκp?<0.

For scalar theories accommodating spherically symmetric Q-balls, there are also towers of quasi-stable composite Q-balls, called charge swapping Q-balls (CSQs). We investigate the properties, particularly the lifetimes, of these long-lived CSQs in 2+1D and 3+1D using numerical simulations with efficient second order absorbing boundary conditions. We find that the evolution of a CSQ typically consists of 4 distinct stages: initial relaxation, first plateau (CSQ stage), fast decay and second plateau (oscillon stage). We chart the lifetimes of CSQs for different parameters of the initial conditions and of the potential, and show the attractor behavior and other properties of the CSQs.

The chiral magnetic effect for space-time dependent chiral imbalance and magnetic field is explored from AdS/CFT correspondence which relates the AVV three-point function of theN=4super Yang-Mills at strong coupling on the boundary to the Einstein-Maxwell-Chern-Simons theory in the bulk. A formulation of the AVV three point function in terms of Heun functions is developed by an iterative solution of the nonlinear equations of motion in Schwarzschild-AdS5background, which is free from UV/IR divergence. The low-momentum expansion reveals non-local response of the vector current to the chiral imbalance beyond the hydrodynamic approximation and replicates the subtlety of the infrared limit discovered in field theoretic approach in weak coupling. The phenomenological implications to the chiral magnetic effect in the context of relativistic heavy ion collisions are discussed qualitatively.

We derive the off-shell nilpotent and absolutely anticommuting Becchi-Rouet-Stora-Tyutin (BRST), anti-BRST and (anti-)co-BRST symmetry transformations for the Christ--Lee (CL) model in one (0 + 1)-dimension of spacetime by exploiting the (anti-)chiral supervariable approach (ACSA) to BRST formalism where a few specific and appropriate sets of invariant quantities play a decisive role. We prove the nilpotency and absolute anticommutativity properties of the (anti-)BRST and (anti-)co-BRST conserved charges within the framework of ACSA to BRST formalism where we take only one Grassmannian variable into account. We also show the (anti-)BRST and (anti-)co-BRST invariances of the Lagrangian within the framework of ACSA.

Computation of circuit complexity has gained much attention in the Theoretical Physics community in recent times to gain insights about the chaotic features and random fluctuations of fields in the quantum regime. Recent studies of circuit complexity take inspiration from the geometric approach of Nielsen, which itself is based on the idea of optimal quantum control in which a cost function is introduced for the various possible path to determine the optimum circuit. In this paper, we study the relationship between the circuit complexity and Morse theory within the framework of algebraic topology using which we study circuit complexity in supersymmetric quantum field theory describing both simple and inverted harmonic oscillators up to higher orders of quantum corrections. The expression of circuit complexity in quantum regime would then be given by the Hessian of the Morse function in supersymmetric quantum field theory, and try to draw conclusion from their graphical behaviour. We also provide a technical proof of the well known universal connecting relation between quantum chaos and circuit complexity of the supersymmetric quantum field theories, using the general description of Morse theory.

We present new results for classical-particle propagation subject to Lorentz violation. Our analysis is dedicated to spin-nondegenerate operators of arbitrary mass dimension provided by the fermion sector of the Standard-Model Extension. In particular, classical Lagrangians are obtained for the operatorsb^μandH^μνas perturbative expansions in Lorentz violation. The functional dependence of the higher-order contributions in the background fields is found to be quite peculiar, which is probably attributed to particle spin playing an essential role for these cases. This paper closes one of the last gaps in understanding classical-particle propagation in the presence of Lorentz violation. Lagrangians of the kind presented will turn out to be valuable for describing particle propagation in curved backgrounds with diffeomorphism invariance and/or local Lorentz symmetry explicitly violated.

The double copy suggests that the basis of the dynamics of general relativity is Yang-Mills theory. Motivated by the importance of the relativistic two-body problem, we study the classical dynamics of colour-charged particle scattering from the perspective of amplitudes, rather than equations of motion. We explain how to compute the change of colour, and the radiation of colour, during a classical collision. We apply our formalism at next-to-leading order for the colour change and at leading order for colour radiation.

It is a standard result that the integral curves of an auto-parallel vector field are geodesics which, for null and timelike vectors, are the paths of freely-falling particles in general relativity. We introduce a definition of an "auto-parallel" generalised vector field and show that it gives the analogous statements for the classical worldvolumes of strings and branes in arbitrary background field configurations. This appears to give a unified description of the worldvolume equations of strings and branes, similar to the way that generalised geometry provides a unified description of maximal supergravity theories. We present details of the cases of string worldsheets inO(10,10)generalised geometry and M2 branes restricted to the four dimensions ofSL(5,R)?R+generalised geometry. A key quantity is the infinitesimal flow of the conjugate momentum along the generalised tangent vector, which is equated to the gradient of the Hamiltonian, viewed as a function on spacetime.

We investigate configuration-space integrals over punctured Riemann spheres from the viewpoint of the motivic Galois coaction and double-copy structures generalizing the Kawai-Lewellen-Tye (KLT) relations in string theory. For this purpose, explicit bases of twisted cycles and cocycles are worked out whose orthonormality simplifies the coaction. We present methods to efficiently perform and organize the expansions of configuration-space integrals in the inverse string tensionα??or the dimensional-regularization parameterϵof Feynman integrals. Generating-function techniques open up a new perspective on the coaction of multiple polylogarithms in any number of variables and analytic continuations in the unintegrated punctures. We present a compact recursion for a generalized KLT kernel and discuss its origin from intersection numbers of Stasheff polytopes and its implications for correlation functions of two-dimensional conformal field theories. We find a non-trivial example of correlation functions in(p,2)minimal models, which can be normalized to become uniformly transcendental in thep?��?limit.

We propose a novel codimension-n holography, called cone holography, between a gravitational theory ind+1dimensional conical spacetime and a CFT on thed+1?�ndimensional defects. For one general class of solutions, we prove that the cone holography is equivalent to AdS/CFT, by showing that the classical gravitational action and thus the CFT partition function in large N limit are the same for the two theories. We test our proposal by studying Weyl anomaly, Entanglement/Rényi entropy and correlation functions, and find good agreements between the holographic and the CFT results. In particular, the c-theorem is obeyed by cone holography. These are strong supports for our proposal. We discuss two kinds of boundary conditions, the mixed boundary condition and Neumann boundary condition, and find that they both define a consistent theory of cone holography. The cone holography can be regarded as a generalization of the wedge holography, and it is closely related to the defect CFT, entanglement/Rényi entropy and AdS/BCFT(dCFT). Thus it is expected to have a wide range of applications.