479 research outputs found
The Perils of `Soft' SUSY Breaking
We consider a two dimensional SU(N) gauge theory coupled to an adjoint
Majorana fermion, which is known to be supersymmetric for a particular value of
fermion mass. We investigate the `soft' supersymmetry breaking of the discrete
light cone quantization (DLCQ) of this theory. There are several DLCQ
formulations of this theory currently in the literature and they naively appear
to behave differently under `soft' supersymmetry breaking at finite resolution.
We show that all these formulations nevertheless yield identical bound state
masses in the decompactification limit of the light-like circle. Moreover, we
are able to show that the supersymmetry-inspired version of DLCQ (so called
`SDLCQ') provides the best rate of convergence of DLCQ bound state masses
towards the actual continuum values, except possibly near or at the critical
fermion mass. In this last case, we discuss improved extrapolation schemes that
must supplement the DLCQ algorithm in order to obtain correct continuum bound
state masses. Interestingly, when we truncate the Fock space to two particles,
the SDLCQ prescription presented here provides a scheme for improving the rate
of convergence of the massive t'Hooft model. Thus the supersymmetry-inspired
SDLCQ prescription is applicable to theories without supersymmetry.Comment: 11 pages, Latex; 2 figures (EPS); Numerical results extended;
conclusions revise
Bound States of Dimensionally Reduced {SYM}_{2+1} at Finite N
We consider the dimensional reduction of N=1 {SYM}_{2+1} to 1+1 dimensions.
The gauge groups we consider are U(N) and SU(N), where N is finite. We
formulate the continuum bound state problem in the light-cone formalism, and
show that any normalizable SU(N) bound state must be a superposition of an
infinite number of Fock states. We also discuss how massless states arise in
the DLCQ formulation for certain discretizations.Comment: 14 pages, REVTE
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
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
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