Exact Results on Higher Dimensional Quantum Field Theories

Recent work by Zamolodchikov and others has uncovered a kind of "solvable" irrelevant deformation of two dimensional QFT generated by the composite operator T T .The irrelevant composite operator T T is built with the components of the energy-momentum tensor.The T T deformation can be regarded as a peculiar kind of integrable perturbation of integrable quantum field theories (IQFT).In the holographic dual, this deformation represents a geometric cutoff of the asymptotic region of AdS.The QFT is placed on a Dirichlet boundary at finite radial distance in the bulk.In this thesis we consider the problem of exact integration of the T T deformation of two dimensional quantum field theories, as well as some higher dimensional extensions in the form of T T deformations.When the action can be shown to only depend algebraically on the background metric the solution of the deformation equation on the Lagrangian can be given in closed form in terms of solutions of the (extended) Burgers' equation.We present such examples in two and higher dimensions.Recent work by Zamolodchikov and others has uncovered a kind of "solvable" irrelevant deformation of two dimensional QFT generated by the composite operator T T .The irrelevant composite operator T T is built with the components of the energy-momentum tensor.The T T deformation can be regarded as a peculiar kind of integrable perturbation of integrable quantum field theories (IQFT).In the holographic dual, this deformation represents a geometric cutoff of the asymptotic region of AdS.The QFT is placed on a Dirichlet boundary at finite radial distance in the bulk.In this thesis we consider the problem of exact integration of the T T deformation of two dimensional quantum field theories, as well as some higher dimensional extensions in the form of T T deformations.When the action can be shown to only depend algebraically on the background metric the solution of the deformation equation on the Lagrangian can be given in closed form in terms of solutions of the (extended) Burgers' equation.We present such examples in two and higher dimensions.

Sep 20, 20180 citations

Holographic Construction of Quantum Field Theory using Wavelets

Sukhwinder Singh, Gavin K. Brennen

Wavelets encode data at multiple resolutions, which in a wavelet description of a quantum field theory, allows for fields to carry, in addition to space-time coordinates, an extra dimension: scale. A recently introduced Exact Holographic Mapping [C.H. Lee and X.-L. Qi, Phys. Rev. B 93, 035112 (2016)] uses the Haar wavelet basis to represent the free Dirac fermionic quantum field theory (QFT) at multiple renormalization scales thereby inducing an emergent bulk geometry in one higher dimension. This construction is, in fact, generic and we show how higher families of Daubechies wavelet transforms of 1+1 dimensional scalar bosonic QFT generate a bulk description with a variable rate of renormalization flow. In the massless case, where the boundary is described by conformal field theory, the bulk correlations decay with distance consistent with an Anti-de-Sitter space (AdS3) metric whose radius of curvature depends on the wavelet family used. We propose an experimental demonstration of the bulk/boundary correspondence via a digital quantum simulation using Gaussian operations on a set of quantum harmonic oscillator modes.Wavelets encode data at multiple resolutions, which in a wavelet description of a quantum field theory, allows for fields to carry, in addition to space-time coordinates, an extra dimension: scale. A recently introduced Exact Holographic Mapping [C.H. Lee and X.-L. Qi, Phys. Rev. B 93, 035112 (2016)] uses the Haar wavelet basis to represent the free Dirac fermionic quantum field theory (QFT) at multiple renormalization scales thereby inducing an emergent bulk geometry in one higher dimension. This construction is, in fact, generic and we show how higher families of Daubechies wavelet transforms of 1+1 dimensional scalar bosonic QFT generate a bulk description with a variable rate of renormalization flow. In the massless case, where the boundary is described by conformal field theory, the bulk correlations decay with distance consistent with an Anti-de-Sitter space (AdS3) metric whose radius of curvature depends on the wavelet family used. We propose an experimental demonstration of the bulk/boundary correspondence via a digital quantum simulation using Gaussian operations on a set of quantum harmonic oscillator modes.

arXiv:1606.05068Jun 16, 20169 citations

Toward a finite-dimensional formulation of quantum field theory

Miguel Navarro

Foundations of Physics LettersJan 1, 19985 citations

Generalised Hydrodynamics of $\mathrm{T\bar{T}}$ -Deformed Integrable Quantum Field TheoriesGeneralised Hydrodynamics of $\mathrm{T\bar{T}}$-Deformed Integrable Quantum Field Theories

Riccardo Travaglino, Michele Mazzoni, Olalla A. Castro-Alvaredo

In this paper we evaluate the averages of conserved densities and currents associated to charges of generic spin in (1+1)-dimensional massive integrable Quantum Field Theories perturbed by the irrelevant $\mathrm{T\bar{T}}$ operator. By making use of the Thermodynamic Bethe Ansatz approach and of the theory of Generalised Hydrodynamics, we study the non-equilibrium steady state averages of conserved densities and currents in a partitioning protocol. We show that in particular limits, averages can be evaluated exactly in terms of quantities known from the unperturbed theory. In the massless limit we recover known results for the energy and momentum currents and generalise those to any higher spin conserved quantities. We extend some of our results to perturbations of the generalised $\mathrm{T\bar{T}}$ type. For the massive free fermion theory, we find an analytic expression for the effective inverse temperature after at $\mathrm{T\bar{T}}$ perturbation in terms of the bare inverse temperature by making use of Lambert's $W$ function.In this paper we evaluate the averages of conserved densities and currents associated to charges of generic spin in (1+1)-dimensional massive integrable Quantum Field Theories perturbed by the irrelevant $\mathrm{T\bar{T}}$ operator. By making use of the Thermodynamic Bethe Ansatz approach and of the theory of Generalised Hydrodynamics, we study the non-equilibrium steady state averages of conserved densities and currents in a partitioning protocol. We show that in particular limits, averages can be evaluated exactly in terms of quantities known from the unperturbed theory. In the massless limit we recover known results for the energy and momentum currents and generalise those to any higher spin conserved quantities. We extend some of our results to perturbations of the generalised $\mathrm{T\bar{T}}$ type. For the massive free fermion theory, we find an analytic expression for the effective inverse temperature after at $\mathrm{T\bar{T}}$ perturbation in terms of the bare inverse temperature by making use of Lambert's $W$ function.

arXiv:2405.06564May 10, 20240 citations

T\bar{T}

Deformations of Quantum Field theory

Generalised Hydrodynamics of

\mathrm{T\bar{T}}

-Deformed Integrable Quantum Field Theories

\mathrm{T\bar{T}}

operator. By making use of the Thermodynamic Bethe Ansatz approach and of the theory of Generalised Hydrodynamics, we study the non-equilibrium steady state averages of conserved densities and currents in a partitioning protocol. We show that in particular limits, averages can be evaluated exactly in terms of quantities known from the unperturbed theory. In the massless limit we recover known results for the energy and momentum currents and generalise those to any higher spin conserved quantities. We extend some of our results to perturbations of the generalised

\mathrm{T\bar{T}}

type. For the massive free fermion theory, we find an analytic expression for the effective inverse temperature after at

\mathrm{T\bar{T}}

perturbation in terms of the bare inverse temperature by making use of Lambert's

W

function.