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All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Topics in String Theory, Quantum Field Theory And Quantum Gravity

This is the final technical report for DOE Award No. DE-SC0021528 - Topics in string theory, quantum field theory and quantum gravity. The goals of the research program were in three areas - understanding quantum gravity and the internal description of quantum systems using the gauge/gravity correspondence, aspects of entanglement in eld theory, gravity and string theory, and the characterization of the behavior of strongly interacting quantum eld theories. The primary results were on the microscopic understanding of the ER=EPR correspondence as a string duality, and on a matrix model description of the addition of end of the world branes and propagating matter to two dimensional Jackiw-Teitelboim gravity. The former led to the completion of the work shortly after the end of the reporting period and continuing work investigating the properties of the associated stringy black hole microstates. The latter led to the work, which also appeared shortly after the end of the reporting period, and a continuing project to nd a matrix model formulation of the eigenstate thermalization hypothesis and JT gravity with propagating matter.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Artificial dynamical effects in quantum field theory

In Newtonian mechanics, studying a system in a non-Galilean reference frame can lead to inertial pseudoforces appearing, such as the centrifugal force that seems to arise in dynamics analysed in a rotating frame. Likewise, artificial effects may arise in relativistic quantum field theory (QFT) if a system is studied in a framework that violates Poincaré invariance. Here, we highlight how such issues complicate the traditional canonical quantization of QFTs and can lead to a subjective description of natural phenomena. By contrast, the treatment of the same problem using light-front quantization is free from spurious pseudoeffects because Poincaré invariance is effectively preserved for all practical intents and purposes. We illustrate these statements using several examples: the Gerasimov-Drell-Hearn (GDH) relation, a fundamental feature of QFT; the absence of any measurable impact of Lorentz contraction in high-energy collisions; and the fictitious character of vacuum fluctuation contributions to the cosmological constant.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Quantum‐Classical Simulation of Quantum Field Theory by Quantum Circuit Learning

Abstract Quantum circuit learning is employed to simulate quantum field theories (QFTs). Typically, when simulating QFTs with quantum computers, significant challenges are encountered due to the technical limitations of quantum devices when implementing the Hamiltonian using Pauli spin matrices. To address this challenge, quantum circuit learning is leveraged, employing a compact configuration of qubits and low‐depth quantum circuits to predict real‐time dynamics in quantum field theories. The key advantage of this approach is that a single‐qubit measurement can accurately forecast various physical parameters, including fully‐connected operators. To demonstrate the effectiveness of this method, it is used to predict quench dynamics, chiral dynamics and jet production in a 1+1‐dimensional model of quantum electrodynamics. It is found that our predictions closely align with the results of rigorous classical calculations, exhibiting a high degree of accuracy. This hybrid quantum‐classical approach illustrates the feasibility of efficiently simulating large‐scale QFTs on cutting‐edge quantum devices.

Ikeda, Kazuki [Department of Physics University of↗
DOE OSTI2025

Quantum complexity in gravity, quantum field theory, and quantum information science

Quantum complexity quantifies the difficulty of preparing a state or implementing a unitary transformation with limited resources. Applications range from quantum computation to condensed matter physics and quantum gravity. Here, we seek to bridge the approaches of these fields, which define and study complexity using different frameworks and tools. We describe several definitions of complexity, along with their key properties. In quantum information theory, we focus on complexity growth in random quantum circuits. In quantum many-body systems and quantum field theory (QFT), we discuss a geometric definition of complexity in terms of geodesics on the unitary group. In dynamical systems, we explore a definition of complexity in terms of state or operator spreading, as well as concepts from tensor-networks. We also outline applications to simple quantum systems, quantum many-body models, and QFTs including conformal field theories (CFTs). Finally, we explain the proposed relationship between complexity and gravitational observables within the holographic anti-de Sitter (AdS)/CFT correspondence.

Baiguera, Stefano [Istituto Nazionale di Fisica Nu↗
DOE OSTI2025

Qubit Regularization of Quantum Field Theories

To study quantum field theories on a quantum computer, we must begin with Hamiltonians defined on a finite-dimensional Hilbert space and then take appropriate limits. This approach can be seen as a new type of regularization for quantum field theories, which we refer to as qubit regularization. A related finite-dimensional regularization, known as the D-theory approach, was proposed long ago as a general framework for all quantum field theories. In this framework, the dimensionality of the local Hilbert space at each spatial point can increase as needed through an additional flavor index. To reproduce asymptotically free QFTs, most studies assume that qubit-regularized theories require extending the local Hilbert space to infinity. However, contrary to this common belief, recent discoveries in (1+1) dimensions have revealed two examples where asymptotic freedom appears to emerge within a strictly finite-dimensional local Hilbert space through a novel renormalization group (RG) flow. These findings motivate further investigation into whether asymptotically free gauge theories could also emerge within a strictly finite-dimensional local Hilbert space. To support these explorations, we propose an orthonormal basis called the monomer-dimer-tensor-network (MDTN) basis and use it to construct new types of qubit-regularized lattice gauge theories.

Chandrasekharan, Shailesh [Duke Univ., Durham, NC ↗
DOE OSTI2022

Research in Quantum Field Theory, Cosmology, and String Theory

This project covered research in theoretical high energy physics at Brandeis University by PI Albion Lawrence and Co-PIs Matthew Headrick and Howard Schnitzer. The work of Albion Lawrence covered quantum field theoretic models of cosmic inflation and of quintessence-type dark energy, consistent with constraints on quantum gravity; the dynamics of open quantum systems, with an eye towards applications to holography; and the application of quantum information theory – particularly measures of quantum entanglement – to quantum field theories and quantum gravity. The work of Matthew Headrick covered the intersection of quantum information theory and quantum gravity, with a focus on the holographic encoding of quantum information theoretic concepts such as entanglement and computational complexity in field theory. Headrick also achieved significant technical results in closed string field theory. The work of Howard Schnitzer covered the computation of quantum information theoretic quantities in quantum field theories.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Variational Neural-Network Ansatz for Continuum Quantum Field Theory

Physicists dating back to Feynman have lamented the difficulties of applying the variational principle to quantum field theories. In nonrelativistic quantum field theories, the challenge is to parametrize and optimize over the infinitely many n-particle wave functions comprising the state’s Fock-space representation. Here we approach this problem by introducing neural-network quantum field states, a deep learning ansatz that enables application of the variational principle to nonrelativistic quantum field theories in the continuum. Our ansatz uses the Deep Sets neural network architecture to simultaneously parametrize all of the n-particle wave functions comprising a quantum field state. We employ our ansatz to approximate ground states of various field theories, including an inhomogeneous system and a system with long-range interactions, thus demonstrating a powerful new tool for probing quantum field theories.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Multiparticle interpolating operators in quantum field theories with cubic symmetry

Numerical studies of lattice quantum field theories are conducted in finite spatial volumes, typically with cubic symmetry in the spatial coordinates. Motivated by these studies, this work presents a general algorithm to construct multiparticle interpolating operators for quantum field theories with cubic symmetry. The algorithm automates the block diagonalization required to combine multiple operators of definite linear momentum into irreducible representations of the appropriate little group. Examples are given for distinguishable and indistinguishable particles including cases with both zero and nonzero spin.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Entanglement Renormalization for Quantum Field Theories with Discrete Wavelet Transforms

We propose an adaptation of Entanglement Renormalization for quantum field theories that, through the use of discrete wavelet transforms, strongly parallels the tensor network architecture of the Multiscale Entanglement Renormalization Ansatz (a.k.a. MERA). Our approach, called wMERA, has several advantages of over previous attempts to adapt MERA to continuum systems. In particular, (i) wMERA is formulated directly in position space, hence preserving the quasi-locality and sparsity of entanglers; and (ii) it enables a built-in RG flow in the implementation of real-time evolution and in computations of correlation functions, which is key for efficient numerical implementations. As examples, we describe in detail two concrete implementations of our wMERA algorithm for free scalar and fermionic theories in (1+1) spacetime dimensions. Possible avenues for constructing wMERAs for interacting field theories are also discussed.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

New Tools for Strongly Coupled Quantum Field Theories

This project involves the study of Quantum field theory (QFT), especially strongly coupled QFTs that are not amenable to conventional perturbative techniques. The unifying goal of the project is the development and application of new tools for analyzing strongly coupled QFTs. These tools are ultimately based on different notions of global symmetries.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Universal fine grained asymptotics of free and weakly coupled quantum field theory

We give a rigorous proof that in any free quantum field theory with a finite group global symmetry G, on a compact spatial manifold, at sufficiently high energy, the density of states ρ α (E) for each irreducible representation α of G obeys a universal formula as conjectured by Harlow and Ooguri. We further prove that this continues to hold in a weakly coupled quantum field theory, given an appropriate scaling of the coupling with temperature. This generalizes similar results that were previously obtained in (1 + 1)-D to higher spacetime dimension. We discuss the role of averaging in the density of states, and we compare and contrast with the case of continuous group G, where we prove a universal, albeit different, behavior.

Discrete Symmetries↗
DOE OSTI2023

Determining all thermodynamic transport coefficients for an interacting large N quantum field theory

Thermodynamic transport coefficients can be calculated directly from quantum field theory without requiring analytic continuation to real time. We determine all second-order thermodynamic transport coefficients for the uncharged N-component massless (critical) scalar field theory with quartic interaction in the large N limit, for any value of the coupling. We find that in the large N limit, all thermodynamic transport coefficients for the interacting theory can be expressed analytically in terms of the in-medium mass and sums over modified Bessel functions. We expect our technique to allow a similar determination of all thermodynamic transport coefficients for all theories that are solvable in the large N limit, including certain gauge theories.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Emergence of quantum-field theory in causal diamonds

The experimental successes of quantum-field theory do not justify using it to describe even a finite fraction of the entanglement entropy of a causal diamond with its exterior, in the limit of large diamonds. Susskind and Uglum and Jacobson conjectured that this divergent entropy could be thought of as a renormalization of Newton’s constant in the Bekenstein–Hawking formula, if we applied that formula to arbitrary causal diamonds. Jacobson showed that this leads to a derivation of the null projection of Einstein’s equations as the hydrodynamic equations of the area law for arbitrary diamonds, a derivation which has the added virtue of demonstrating that the cosmological constant is not an energy density. Using a gauge choice adapted to causal diamond boundaries, we revisit arguments of Carlip and Solodukhin that the proper theory of near horizon states is a (cut-off) (1 + 1)-dimensional conformal field theory, with central charge proportional to the transverse area. This leads to a universal formula for fluctuations of the modular Hamiltonian of a diamond, which we argue is compatible with the explanation of the temperature of de Sitter space in terms of an identification between localized energy and the number of constrained q-bits of the holographic degrees of freedom.

Astronomy & Astrophysics↗
DOE OSTI2022

Interacting fractons in 2+1-dimensional quantum field theory

We analyze, in perturbation theory, a theory of weakly interacting fractons and non-relativistic fermions in a 2+1 dimensional Quantum Field Theory. In particular we compute the 1-loop corrections to the self energies and interaction vertex, and calculate the associated 1-loop Renormalization Group flows of the coupling constants. Surprisingly, we find that the fracton-fermion coupling does not flow due to an emergent coordinate-dependent symmetry of the effective Lagrangian, making this model a well-defined quantum field theory. We provide additional discussions on the regularization and renormalization of interacting fractonic theories, as well as both qualitative and quantitative remarks regarding the theory at finite temperature and finite chemical potential.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1980

Numerical methods for studying anharmonic oscillator approximations to the phi super 4 sub 2 quantum field theory

This paper is an expanded version of a talk given at the 1979 T.I.C.O.M. conference. It is a self-contained introduction, for applied mathematicians and numerical analysts, to quantum mechanics and quantum field theory. It also contains a brief description of the authors' numerical approach to the problems of quantum field theory, which may best be summarized by the question; Can we compute the eigenvalues and eigenfunctions of Schrodinger operators in infinitely many variables.

Isaacson, D.↗
DOE OSTI2024

Topological symmetry in quantum field theory

We introduce a definition and framework for internal topological symmetries in quantum field theory, including “noninvertible symmetries” and “categorical symmetries”. We outline a calculus of topological defects which takes advantage of well-developed theorems and techniques in topological field theory. Our discussion focuses on finite symmetries, and we give indications for a generalization to other symmetries. We treat quotients and quotient defects (often called “gauging” and “condensation defects”), finite electromagnetic duality, and duality defects, among other topics. We include an appendix on finite homotopy theories, which are often used to encode finite symmetries and for which computations can be carried out using methods of algebraic topology. Throughout we emphasize exposition and examples over a detailed technical treatment.

Mathematics↗