585 research outputs found
Iterative Solution of the Supereigenvalue Model
An integral form of the discrete superloop equations for the supereigenvalue
model of Alvarez-Gaume, Itoyama, Manes and Zadra is given. By a change of
variables from coupling constants to moments we find a compact form of the
planar solution for general potentials. In this framework an iterative scheme
for the calculation of higher genera contributions to the free energy and the
multi-loop correlators is developed. We present explicit results for genus one.Comment: 21 pages, LaTeX, no figure
The Supereigenvalue Model in the Double-Scaling Limit
The double-scaling limit of the supereigenvalue model is performed in the
moment description. This description proves extremely useful for the
identification of the multi-critical points in the space of bosonic and
fermionic coupling constants. An iterative procedure for the calculation of
higher-genus contributions to the free energy and to the multi-loop correlators
in the double-scaling limit is developed. We present the general structure of
these quantities at genus g and give explicit results up to and including genus
two.Comment: 19 pages, LaTe
A Simple Algebraic Derivation of the Covariant Anomaly and Schwinger Term
An expression for the curvature of the "covariant" determinant line bundle is
given in even dimensional space-time. The usefulness is guaranteed by its
prediction of the covariant anomaly and Schwinger term. It allows a parallel
derivation of the consistent anomaly and Schwinger term, and their covariant
counterparts, which clarifies the similarities and differences between them. In
particular, it becomes clear that in contrary to the case for anomalies, the
difference between the consistent and covariant Schwinger term can not be
extended to a local form on the space of gauge potentials.Comment: 16 page
Hamiltonian Interpretation of Anomalies
A family of quantum systems parametrized by the points of a compact space can realizeits classical symmetries via a new kind of nontrivial ray representation. We show that thisphenomenon in fact occurs for the quantum mechanics of fermions in the presence ofbackground gauge fields, and is responsible for both the nonabelian anomaly and Witten’sSU(2) anomaly. This provides a hamiltonian interpretation of anomalies: in the affectedtheories Gauss’ law cannot be implemented. The analysis clearly shows why there are nofurther obstructions corresponding to higher spheres in configuration space, in agreementwith a recent result of Atiyah and Singer
Comments on Supersymmetric Vector and Matrix Models
Some results in random matrices are generalized to supermatrices, in
particular supermatrix integration is reduced to an integration over the
eigenvalues and the resulting volume element is shown to be equivalent to a one
dimensional Coulomb gas of both positive and negative charges.It is shown
that,for polynomial potentials, after removing the instability due to the
annihilation of opposite charges, supermatrix models are indistinguishable from
ordinary matrix models, in agreement with a recent result by Alvarez-Gaume and
Manes. It is pointed out however that this may not be true for more general
potentials such as for instance the supersymmetric generalization of the Penner
model.Comment: 6 page
On the Semi-Relative Condition for Closed (TOPOLOGICAL) Strings
We provide a simple lagrangian interpretation of the meaning of the
semi-relative condition in closed string theory. Namely, we show how the
semi-relative condition is equivalent to the requirement that physical
operators be cohomology classes of the BRS operators acting on the space of
local fields {\it covariant} under world-sheet reparametrizations. States
trivial in the absolute BRS cohomology but not in the semi-relative one are
explicitly seen to correspond to BRS variations of operators which are not
globally defined world-sheet tensors. We derive the covariant expressions for
the observables of topological gravity. We use them to prove a formula that
equates the expectation value of the gravitational descendant of ghost number 4
to the integral over the moduli space of the Weil-Peterson K\"ahler form.Comment: 10 pages, harvmac, CERN-TH-7084/93, GEF-TH-21/199
Strong Constraints on the Parameter Space of the MSSM from Charge and Color Breaking Minima
A complete analysis of all the potentially dangerous directions in the
field-space of the minimal supersymmetric standard model is carried out. They
are of two types, the ones associated with the existence of charge and color
breaking minima in the potential deeper than the realistic minimum and the
directions in the field-space along which the potential becomes unbounded from
below. The corresponding new constraints on the parameter space are given in an
analytic form, representing a set of necessary and sufficient conditions to
avoid dangerous directions. They are very strong and, in fact, there are
extensive regions in the parameter space that become forbidden. This produces
important bounds, not only on the value of , but also on the values of
and . Finally, the crucial issue of the one-loop corrections to the
scalar potential has been taken into account in a proper way.Comment: 48 pages, LaTeX, 12 uuencoded postscript figures in additional file.
Only a small comment about the m=0 (no-scale) limit has been included in
sect.6 (Results) and sect.7 (Conclusions
The N=4 string is the same as the N=2 string
We redo the quantization of the N=4 string, taking into account the
reducibility of the constraints. The result is equivalent to the N=2 string,
with critical dimension D=4 and signature (++--). The N=4 formulation has
several advantages: the sigma-model field equations are implied classically,
rather than by quantum/beta-function calculations; self-duality/chirality is
one of the super-Virasoro constraints; SO(2,2) covariance is manifest. This
reveals that the theory includes fermions, and is apparently spacetime
supersymmetric.Comment: 7 pg (uuencoded dvi file; otherwise same as original
Bosonisation and Duality Symmetry in the Soldering Formalism
We develop a technique that solders the dual aspects of some symmetry. Using
this technique it is possible to combine two theories with such symmetries to
yield a new effective theory. Some applications in two and three dimensional
bosonisation are discussed. In particular, it is shown that two apparently
independent three dimensional massive Thirring models with same coupling but
opposite mass signatures, in the long wavelegth limit, combine by the process
of bosonisation and soldering to yield an effective massive Maxwell theory.
Similar features also hold for quantum electrodynamics in three dimensions. We
also provide a systematic derivation of duality symmetric actions and show that
the soldering mechanism leads to a master action which is duality invariant
under a bigger set of symmetries than is usually envisaged. The concept of
duality swapping is introduced and its implications are analysed. The example
of electromagnetic duality is discussed in details.Comment: LaTex file, 38 pages, this paper is a revised combination of
hep-th/9709105 and hep-th/9710060. Ref-Journal: Nucl. Phys. B, to appea
Derivation of Index Theorems by Localization of Path Integrals
We review the derivation of the Atiyah-Singer and Callias index theorems
using the recently developed localization method to calculate exactly the
relevant supersymmetric path integrals. (Talk given at the III International
Conference on Mathematical Physics, String Theory and Quantum Gravity, Alushta,
Ukraine, June 13-24, 1993)Comment: 11 pages in LaTeX, HU-TFT-93-3
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