391 research outputs found
Numerical evidence for the Maldacena conjecture in two-dimensional N=(8,8) super Yang-Mills theory
The N=(8,8) super Yang-Mills theory in 1+1 dimensions is solved at strong
coupling to directly confirm the predictions of supergravity at weak coupling.
The calculations are done in the large-N_c approximation using Supersymmetric
Discrete Light-Cone Quantization. The stress-energy correlator is obtained as a
function of the separation r; for intermediate values of r, the correlator
behaves in a manner consistent with the 1/r^5 behavior predicted by
weak-coupling supergravity.Comment: 6 pages, 3 figures; requires espcrc2.sty; to appear in the
proceedings of the Workshop on Light-Cone QCD and Nonperturbative Hadron
Physics, Cairns, Australia, July 7-15, 200
Numerical Simulations of N=(1,1) SYM{1+1} with Large Supersymmetry Breaking
We consider the SYM theory that is obtained by dimensionally
reducing SYM theory in 2+1 dimensions to 1+1 dimensions and discuss soft
supersymmetry breaking. We discuss the numerical simulation of this theory
using SDLCQ when either the boson or the fermion has a large mass. We compare
our result to the pure adjoint fermion theory and pure adjoint boson DLCQ
calculations of Klebanov, Demeterfi, and Bhanot and of Kutasov. With a large
boson mass we find that it is necessary to add additional operators to the
theory to obtain sensible results. When a large fermion mass is added to the
theory we find that it is not necessary to add operators to obtain a sensible
theory. The theory of the adjoint boson is a theory that has stringy bound
states similar to the full SYM theory. We also discuss another theory of
adjoint bosons with a spectrum similar to that obtained by Klebanov, Demeterfi,
and Bhanot.Comment: 12 pages, 4 figure
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).Comment: 14 pages, 3 figures, LaTe
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.Comment: 20pp., 21 figure
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.Comment: 18pp. 7 figures, uses REVTe
Improved results for N=(2,2) super Yang-Mills theory using supersymmetric discrete light-cone quantization
We consider the (1+1)-dimensional super Yang--Mills theory
which is obtained by dimensionally reducing super Yang--Mills
theory in four dimension to two dimensions. We do our calculations in the
large- approximation using Supersymmetric Discrete Light Cone
Quantization. The objective is to calculate quantities that might be
investigated by researchers using other numerical methods. We present a
precision study of the low-mass spectrum and the stress-energy correlator
. We find that the mass gap of this theory closes as the
numerical resolution goes to infinity and that the correlator in the
intermediate region behaves like .Comment: 18 pages, 8 figure
Towards a SDLCQ test of the Maldacena Conjecture
We consider the Maldacena conjecture applied to the near horizon geometry of
a D1-brane in the supergravity approximation and present numerical results of a
test of the conjecture against the boundary field theory calculation using
DLCQ. We previously calculated the two-point function of the stress-energy
tensor on the supergravity side; the methods of Gubser, Klebanov, Polyakov, and
Witten were used. On the field theory side, we derived an explicit expression
for the two-point function in terms of data that may be extracted from the
supersymmetric discrete light cone quantization (SDLCQ) calculation at a given
harmonic resolution. This yielded a well defined numerical algorithm for
computing the two-point function. For the supersymmetric Yang-Mills theory with
16 supercharges that arises in the Maldacena conjecture, the algorithm is
perfectly well defined; however, the size of the numerical computation
prevented us from obtaining a numerical check of the conjecture. We now present
numerical results with approximately 1000 times as many states as we previously
considered. These results support the Maldacena conjecture and are within
of the predicted numerical results in some regions. Our results are
still not sufficient to demonstrate convergence, and, therefore, cannot be
considered to a numerical proof of the conjecture. We present a method for
using a ``flavor'' symmetry to greatly reduce the size of the basis and discuss
a numerical method that we use which is particularly well suited for this type
of matrix element calculation.Comment: 10 pages, 1 figur
Application of Pauli-Villars regularization and discretized light-cone quantization to a single-fermion truncation of Yukawa theory
We apply Pauli-Villars regularization and discretized light-cone quantization
to the nonperturbative solution of (3+1)-dimensional Yukawa theory in a
single-fermion truncation. Three heavy scalars, including two with negative
norm, are used to regulate the theory. The matrix eigenvalue problem is solved
for the lowest-mass state with use of a new, indefinite-metric Lanczos
algorithm. Various observables are extracted from the wave functions, including
average multiplicities and average momenta of constituents, structure
functions, and a form factor slope.Comment: 21 pages, 7 figures, RevTeX; published version: more extensive data
in the tables of v
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.Comment: 35 pages, elsart.cls, 3 figure
Casimir energy of a compact cylinder under the condition
The Casimir energy of an infinite compact cylinder placed in a uniform
unbounded medium is investigated under the continuity condition for the light
velocity when crossing the interface. As a characteristic parameter in the
problem the ratio is used, where and
are, respectively, the permittivity and permeability of the material
making up the cylinder and and are those for the
surrounding medium. It is shown that the expansion of the Casimir energy in
powers of this parameter begins with the term proportional to . The
explicit formulas permitting us to find numerically the Casimir energy for any
fixed value of are obtained. Unlike a compact ball with the same
properties of the materials, the Casimir forces in the problem under
consideration are attractive. The implication of the calculated Casimir energy
in the flux tube model of confinement is briefly discussed.Comment: REVTeX, 12 pages, 1 figure in a separate fig1.eps file, 1 table;
minor corrections in English and misprints; version to be published in Phys.
Rev. D1
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