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J. R. Hiller

Publications and source records attributed to J. R. Hiller.

At least 55 records · Page 3Linked to original sources
arXiv2005

Direct evidence for the Maldacena conjecture for N=(8,8) super Yang-Mills theory in 1+1 dimensions

We solve N=(8,8) super Yang-Mills theory in 1+1 dimensions at strong coupling to directly confirm the predictions of supergravity at weak coupling. We do our calculations in the large-N_c approximation using Supersymmetric Discrete Light-Cone Quantization with up to 3*10^{12} basis states. We calculate the stress-energy correlator as a function of the separation r and find that at intermediate values of r the correlator behaves as r^{-5} to within errors as predicted by weak-coupling supergravity. We also present an extension to significantly higher resolution of our earlier results for the same correlator in the N=(2,2) theory and see that in this theory the correlator has very different behavior at intermediate values of r.

hep-th↗
arXiv2004

Two-dimensional super Yang-Mills theory investigated with improved resolution

In earlier work, N=(1,1) super Yang--Mills theory in two dimensions was found to have several interesting properties, though these properties could not be investigated in any detail. In this paper we analyze two of these properties. First, we investigate the spectrum of the theory. We calculate the masses of the low-lying states using the supersymmetric discrete light-cone (SDLCQ) approximation and obtain their continuum values. The spectrum exhibits an interesting distribution of masses, which we discuss along with a toy model for this pattern. We also discuss how the average number of partons grows in the bound states. Second, we determine the number of fermions and bosons in the N=(1,1) and N=(2,2) theories in each symmetry sector as a function of the resolution. Our finding that the numbers of fermions and bosons in each sector are the same is part of the answer to the question of why the SDLCQ approximation exactly preserves supersymmetry.

hep-th↗
arXiv2004

Nonperturbative solution of Yukawa theory and gauge theories

Recent progress in the nonperturbative solution of (3+1)-dimensional Yukawa theory and quantum electrodynamics (QED) and (1+1)-dimensional super Yang-Mills (SYM) theory will be summarized. The work on Yukawa theory has been extended to include two-boson contributions to the dressed fermion state and has inspired similar work on QED, where Feynman gauge has been found surprisingly convenient. In both cases, the theories are regulated in the ultraviolet by the inclusion of Pauli-Villars particles. For SYM theory, new high-resolution calculations of spectra have been used to obtain thermodynamic functions and improved results for a stress-energy correlator.

hep-ph↗
arXiv2004

A nonperturbative calculation of the electron's magnetic moment

In principle, the complete spectrum and bound-state wave functions of a quantum field theory can be determined by finding the eigenvalues and eigensolutions of its light-cone Hamiltonian. One of the challenges in obtaining nonperturbative solutions for gauge theories such as QCD using light-cone Hamiltonian methods is to renormalize the theory while preserving Lorentz symmetries and gauge invariance. For example, the truncation of the light-cone Fock space leads to uncompensated ultraviolet divergences. We present two methods for consistently regularizing light-cone-quantized gauge theories in Feynman and light-cone gauges: (1) the introduction of a spectrum of Pauli-Villars fields which produces a finite theory while preserving Lorentz invariance; (2) the augmentation of the gauge-theory Lagrangian with higher derivatives. In the latter case, which is applicable to light-cone gauge (A^+ = 0), the A^- component of the gauge field is maintained as an independent degree of freedom rather than a constraint. Finite-mass Pauli-Villars regulators can also be used to compensate for neglected higher Fock states. As a test case, we apply these regularization procedures to an approximate nonperturbative computation of the anomalous magnetic moment of the electron in QED as a first attempt to meet Feynman's famous challenge.

hep-ph↗
arXiv2003

The covariant structure of light-front wave functions and the behavior of hadronic form factors

We study the analytic structure of light-front wave functions (LFWFs) and its consequences for hadron form factors using an explicitly Lorentz-invariant formulation of the front form. The normal to the light front is specified by a general null vector $ω^μ.$ The LFWFs with definite total angular momentum are eigenstates of a {\it kinematic} angular momentum operator and satisfy all Lorentz symmetries. They are analytic functions of the invariant mass squared of the constituents $M^2_0= (\sum k^μ)^2$ and the light-cone momentum fractions $x_i= {k_i\cd ω/ p \cd ω}$ multiplied by invariants constructed from the spin matrices, polarization vectors, and $ω^μ.$ These properties are illustrated using known nonperturbative eigensolutions of the Wick--Cutkosky model. We analyze the LFWFs introduced by Chung and Coester to describe static and low momentum properties of the nucleons. They correspond to the spin-locking of a quark with the spin of its parent nucleon, together with a positive-energy projection constraint. These extra constraints lead to anomalous dependence of form factors on $Q$ rather than $Q^2.$ In contrast, the dependence of LFWFs on $M^2_0$ implies that hadron form factors are analytic functions of $Q^2$ in agreement with dispersion theory and perturbative QCD. We show that a model incorporating the leading-twist perturbative QCD prediction is consistent with recent data for the ratio of proton Pauli and Dirac form factors.

hep-ph↗
arXiv2003

Single-Spin Polarization Effects and the Determination of Timelike Proton Form Factors

We show that measurements of the proton's polarization in electron-positron annihilation to a proton-antiproton pair $e^+ e^- \to p \bar p$ strongly discriminate between the analytic forms of models which fit the proton form factors in the spacelike region. In particular, the single-spin asymmetry normal to the scattering plane measures the relative phase difference between the timelike $G_E$ and $G_M$ form factors. The expected proton polarization in the timelike region is large, of order of several tens of percent.

hep-ph↗
arXiv2003

Nonperturbative light-front methods

Two methods for the nonperturbative solution of field-theoretic bound-state problems, based on light-front coordinates, are briefly reviewed. One uses Pauli-Villars regularization and the other supersymmetry. Applications to Yukawa theory and super Yang-Mills theory with fundamental matter are emphasized.

hep-ph↗
arXiv2003

Hard Photodisintegration of a Proton Pair in 3He

Hard photodisintegration of the deuteron has been extensively studied in order to understand the dynamics of the transition from hadronic to quark-gluon descriptions of the strong interaction. In this work, we discuss the extension of this program to hard photodisintegration of a $pp$ pair in the $^3$He nucleus. Experimental confirmation of new features predicted here for the suggested reaction would advance our understanding of hard nuclear reactions. A main prediction, in contrast with low-energy observations, is that the $pp$ breakup cross section is not much smaller than the one for $pn$ break up.In some models, the energy-dependent oscillations observed for $pp$ scattering are predicted to appear in the $γ^3{\rm He} \to p p + n$ reaction. Such an observation would open up a completely new field in studies of color coherence phenomena in hard nuclear reactions. We also demonstrate that, in addition to the energy dependence, the measurement of the light-cone momentum distribution of the recoil neutron provides an independent test of the underlying dynamics of hard disintegration.

nucl-th↗
arXiv2003

Spectrum of N=1 massive super Yang-Mills theory with fundamental matter in 1+1 dimensions

We consider N=1 supersymmetric Yang-Mills theory with fundamental matter in the large-N_c approximation in 1+1 dimensions. We add a Chern-Simons term to give the adjoint partons a mass and solve for the meson bound states. Here ``mesons'' are color-singlet states with two partons in the fundamental representation. The spectrum is exactly supersymmetric, and there is complete degeneracy between the fermion and boson bound states. We find that the mass spectrum is composed of two distinct bands. We analyze the properties of the bound states in each band and find a number of interesting properties of these states. In both bands, some of the states are nearly pure quark-gluon bound states while others are nearly pure squark-gluon bound states. The structure functions of many of the bound states found are very strongly peaked near x=0. The convergence of the numerical approximation appears to be very good in all cases.

hep-ph↗
arXiv2003

The mass renormalization of nonperturbative light-front Hamiltonian theory: An illustration using truncated, Pauli-Villars-regulated Yukawa interactions

We obtain analytic, nonperturbative, approximate solutions of Yukawa theory in the one-fermion sector using light-front quantization. The theory is regulated in the ultraviolet by the introduction of heavy Pauli-Villars scalar and fermion fields, each with negative norm. In order to obtain a directly soluble problem, fermion-pair creation and annihilation are neglected, and the number of bosonic constituents is limited to one of either type. We discuss some of the features of the wave function of the eigensolution, including its endpoint behavior and spin and orbital angular momentum content. The limit of infinite Pauli-Villars mass receives special scrutiny.

hep-th↗
arXiv2003

Anomalously light mesons in a (1+1)-dimensional supersymmetric theory with fundamental matter

We consider N=1 supersymmetric Yang-Mills theory with fundamental matter in the large-N_c approximation in 1+1 dimensions. We add a Chern-Simons term to give the adjoint partons a mass and solve for the meson bound states. Here mesons are color-singlet states with two partons in the fundamental representation but are not necessarily bosons. We find that this theory has anomalously light meson bound states at intermediate and strong coupling. We also examine the structure functions for these states and find that they prefer to have as many partons as possible at low longitudinal momentum fraction.

hep-ph↗
arXiv2002

Properties of the Bound States of Super-Yang-Mills-Chern-Simons Theory

We apply supersymmetric discrete light-cone quantization (SDLCQ) to the study of supersymmetric Yang-Mills-Chern-Simons (SYM-CS) theory on R x S^1 x S^1. One of the compact directions is chosen to be light-like and the other to be space-like. Since the SDLCQ regularization explicitly preserves supersymmetry, this theory is totally finite, and thus we can solve for bound-state wave functions and masses numerically without renormalizing. The Chern-Simons term is introduced here to provide masses for the particles while remaining totally within a supersymmetric context. We examine the free, weak and strong-coupling spectrum. The transverse direction is discussed as a model for universal extra dimensions in the gauge sector. The wave functions are used to calculate the structure functions of the lowest mass states. We discuss the properties of Kaluza-Klein states and focus on how they appear at strong coupling. We also discuss a set of anomalously light states which are reflections of the exact Bogomol'nyi-Prasad-Sommerfield states of the underlying SYM theory.

hep-th↗
arXiv2002

Nonperturbative solution of supersymmetric gauge theories

Recent work on the numerical solution of supersymmetric gauge theories is described. The method used is SDLCQ (supersymmetric discrete light-cone quantization). An application to N=1 supersymmetric Yang-Mills theory in 2+1 dimensions at large N_c is summarized. The addition of a Chern-Simons term is also discussed.

hep-th↗
arXiv2002

Anomalously light states in super-Yang-Mills Chern-Simons theory

Inspired by our previous finding that supersymmetric Yang-Mills-Chern-Simons (SYM-CS) theory dimensionally reduced to 1+1 dimensions possesses approximate Bogomol'nyi-Prasad-Sommerfield (BPS) states, we study the analogous phenomenon in the three-dimensional theory. Approximate BPS states in two dimensions have masses which are nearly independent of the Yang-Mills coupling and proportional to their average number of partons. These states are a reflection of the exactly massless BPS states of the underlying pure SYM theory. In three dimensions we find that this mechanism leads to anomalously light bound states. While the mass scale is still proportional to the average number of partons times the square of the CS coupling, the average number of partons in these bound states changes with the Yang-Mills coupling. Therefore, the masses of these states are not independent of the coupling. Our numerical calculations are done using supersymmetric discrete light-cone quantization (SDLCQ).

hep-th↗
arXiv2002

Approximate BPS states

We consider dimensionally reduced three-dimensional supersymmetric Yang-Mills-Chern-Simons theory. Although the N=1 supersymmetry of this theory does not allow true massive Bogomol'nyi-Prasad-Sommerfield (BPS) states, we find approximate BPS states which have non-zero masses that are almost independent of the Yang-Mills coupling constant and which are a reflection of the massless BPS states of the underlying N=1 super Yang-Mills theory. The masses of these states at large Yang-Mills coupling are exactly at the n-particle continuum thresholds. This leads to a relation between their masses at zero and large Yang-Mills coupling.

hep-th↗
arXiv2001

Simulation of Dimensionally Reduced SYM-Chern-Simons Theory

A supersymmetric formulation of a three-dimensional SYM-Chern-Simons theory using light-cone quantization is presented, and the supercharges are calculated in light-cone gauge. The theory is dimensionally reduced by requiring all fields to be independent of the transverse dimension. The result is a non-trivial two-dimensional supersymmetric theory with an adjoint scalar and an adjoint fermion. We perform a numerical simulation of this SYM-Chern-Simons theory in 1+1 dimensions using SDLCQ (Supersymmetric Discrete Light-Cone Quantization). We find that the character of the bound states of this theory is very different from previously considered two-dimensional supersymmetric gauge theories. The low-energy bound states of this theory are very ``QCD-like.'' The wave functions of some of the low mass states have a striking valence structure. We present the valence and sea parton structure functions of these states. In addition, we identify BPS-like states which are almost independent of the coupling. Their masses are proportional to their parton number in the large-coupling limit.

hep-th↗
arXiv2001

Wave functions and spectra from (S)DLCQ

Applications of discretized light-cone quantization (DLCQ) to (3+1)-dimensional Yukawa theory with Pauli-Villars regulators and of supersymmetric DLCQ (SDLCQ) to (2+1)-dimensional super Yang-Mills theory are discussed. The ability of these methods to provide wave functions as well as spectra is emphasized.

hep-ph↗