735 research outputs found
Seiberg-Witten prepotential for E-string theory and random partitions
We find a Nekrasov-type expression for the Seiberg-Witten prepotential for
the six-dimensional non-critical E_8 string theory toroidally compactified down
to four dimensions. The prepotential represents the BPS partition function of
the E_8 strings wound around one of the circles of the toroidal
compactification with general winding numbers and momenta. We show that our
expression exhibits expected modular properties. In particular, we prove that
it obeys the modular anomaly equation known to be satisfied by the
prepotential.Comment: 14 page
Seiberg-Witten prepotential for E-string theory and global symmetries
We obtain Nekrasov-type expressions for the Seiberg-Witten prepotential for
the six-dimensional (1,0) supersymmetric E-string theory compactified on T^2
with nontrivial Wilson lines. We consider compactification with four general
Wilson line parameters, which partially break the E_8 global symmetry. In
particular, we investigate in detail the cases where the Lie algebra of the
unbroken global symmetry is E_n + A_{8-n} with n=8,7,6,5 or D_8. All our
Nekrasov-type expressions can be viewed as special cases of the elliptic
analogue of the Nekrasov partition function for the SU(N) gauge theory with
N_f=2N flavors. We also present a new expression for the Seiberg-Witten curve
for the E-string theory with four Wilson line parameters, clarifying the
connection between the E-string theory and the SU(2) Seiberg-Witten theory with
N_f=4 flavors.Comment: 22 pages. v2: comments and a reference added, version to appear in
JHE
The Heavy Quark Potential in Two-Dimentional QCD with Adjoint Matter
Using a loop formulation approach of QCD, we study the potential between
two heavy quarks in the presence of adjoint scalar fields, and demonstrate how
't Hooft's planar rule is manifested in this formulation. Based on some
physical assumptions, we argue that large adjoint loops ``confined'' inside an
external fundamental one give a Casimir type contribution to the potential
energy, while the small loops only renormalize the string tension. We also
extend the results to the case of massive adjoint fields.Comment: 24 pages phyzzx (6 figures available upon request), USITP-94-1
From polymers to quantum gravity: triple-scaling in rectangular matrix models
Rectangular matrix models can be solved in several qualitatively
distinct large limits, since two independent parameters govern the size of
the matrix. Regarded as models of random surfaces, these matrix models
interpolate between branched polymer behaviour and two-dimensional quantum
gravity. We solve such models in a `triple-scaling' regime in this paper, with
and becoming large independently. A correspondence between phase
transitions and singularities of mappings from to is
indicated. At different critical points, the scaling behavior is determined by:
i) two decoupled ordinary differential equations; ii) an ordinary differential
equation and a finite difference equation; or iii) two coupled partial
differential equations. The Painlev\'e II equation arises (in conjunction with
a difference equation) at a point associated with branched polymers. For
critical points described by partial differential equations, there are dual
weak-coupling/strong-coupling expansions. It is conjectured that the new
physics is related to microscopic topology fluctuations.Comment: 29 page
Equivalence of Two Dimensional QCD and the Matrix Model
We consider two dimensional QCD with the spatial dimension compactified to a
circle. We show that the states in the theory consist of interacting strings
that wind around the circle and derive the Hamiltonian for this theory in the
large limit, complete with interactions. Mapping the winding states into
momentum states, we express this Hamiltonian in terms of a continuous field.
For a gauge group with a background source of Wilson loops, we recover
the collective field Hamiltonian found by Das and Jevicki for the matrix
model, except the spatial coordinate is on a circle. We then proceed to show
that two dimensional QCD with a gauge group can be reduced to a one-
dimensional unitary matrix model and is hence equivalent to a theory of
free nonrelativistic fermions on a circle. A similar result is true for the
group , but the fermions must be modded out by the center of mass
coordinate.Comment: 15 pages, CERN-TH 6843/93, UVA-HET-93-0
Symmetry Breaking Phase Transitions in ABJM Theory with a Finite U(1) Chemical Potential
We consider the U(1) charged sector of ABJM theory at finite temperature,
which corresponds to the Reissner-Nordstrom AdS black hole in the dual type IIA
supergravity description. Including back-reaction to the bulk geometry, we show
that phase transitions occur to a broken phase where SU(4) R-symmetry of the
field theory is broken spontaneously by the condensation of dimension one or
two operators. We show both numerically and analytically that the relevant
critical exponents for the dimension one operator agree precisely with those of
mean field theory in the strongly coupled regime of the large N planar limit.Comment: 22 pages, 6 figures, typos corrected, references added, improved
figures, minor changes, accepted for publication in Phys. Rev.
Leading Large N Modification of QCD_2 on a Cylinder by Dynamical Fermions
We consider 2-dimensional QCD on a cylinder, where space is a circle. We find
the ground state of the system in case of massless quarks in a expansion.
We find that coupling to fermions nontrivially modifies the large saddle
point of the gauge theory due to the phenomenon of `decompactification' of
eigenvalues of the gauge field. We calculate the vacuum energy and the vacuum
expectation value of the Wilson loop operator both of which show a nontrivial
dependence on the number of quarks flavours at the leading order in .Comment: 24 pages, TIFR-TH-94/3
String Theoretical Interpretation for Finite N Yang-Mills Theory in Two-Dimensions
We discuss the equivalence between a string theory and the two-dimensional
Yang-Mills theory with SU(N) gauge group for finite N. We find a sector which
can be interpreted as a sum of covering maps from closed string world-sheets to
the target space, whose covering number is less than N. This gives an
asymptotic expansion of 1/N whose large N limit becomes the chiral sector
defined by D.Gross and W.Taylor. We also discuss that the residual part of the
partition function provides the non-perturbative corrections to the
perturbative expansion.Comment: 15 pages, no figures, LaTeX2e, typos corrected, final version to
appear in Modern Physics Letters
Dynamics with Infinitely Many Time Derivatives and Rolling Tachyons
Both in string field theory and in p-adic string theory the equations of
motion involve infinite number of time derivatives. We argue that the initial
value problem is qualitatively different from that obtained in the limit of
many time derivatives in that the space of initial conditions becomes strongly
constrained. We calculate the energy-momentum tensor and study in detail time
dependent solutions representing tachyons rolling on the p-adic string theory
potentials. For even potentials we find surprising small oscillations at the
tachyon vacuum. These are not conventional physical states but rather
anharmonic oscillations with a nontrivial frequency--amplitude relation. When
the potentials are not even, small oscillatory solutions around the bottom must
grow in amplitude without a bound. Open string field theory resembles this
latter case, the tachyon rolls to the bottom and ever growing oscillations
ensue. We discuss the significance of these results for the issues of emerging
closed strings and tachyon matter.Comment: 46 pages, 14 figures, LaTeX. Replaced version: Minor typos corrected,
some figures edited for clarit
The String Theory Approach to Generalized 2D Yang-Mills Theory
We calculate the partition function of the ( and ) generalized
theory defined on an arbitrary Riemann surface. The result which is
expressed as a sum over irreducible representations generalizes the Rusakov
formula for ordinary YM_2 theory. A diagrammatic expansion of the formula
enables us to derive a Gross-Taylor like stringy description of the model. A
sum of 2D string maps is shown to reproduce the gauge theory results. Maps with
branch points of degree higher than one, as well as ``microscopic surfaces''
play an important role in the sum. We discuss the underlying string theory.Comment: TAUP-2182-94, 53 pages of LaTeX and 5 uuencoded eps figure
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