The Complexity of Vector Spin Glasses

We study the annealed complexity of the m-vector spin glasses in the Sherrington-Kirkpatrick limit. The eigenvalue spectrum of the Hessian matrix of the Thouless-Anderson-Palmer (TAP) free energy is found to consist of a continuous band of positive eigenvalues in addition to an isolated eigenvalue and (m-1) null eigenvalues due to rotational invariance. Rather surprisingly, the band does not extend to zero at any finite temperature. The isolated eigenvalue becomes zero in the thermodynamic limit, as in the Ising case (m=1), indicating that the same supersymmetry breaking recently found in Ising spin glasses occurs in vector spin glasses.Comment: 4 pages, 2 figure

The Complexity of Ising Spin Glasses

We compute the complexity (logarithm of the number of TAP states) associated with minima and index-one saddle points of the TAP free energy. Higher-index saddles have smaller complexities. The two leading complexities are equal, consistent with the Morse theorem on the total number of turning points, and have the value given in [A. J. Bray and M. A. Moore, J. Phys. C 13, L469 (1980)]. In the thermodynamic limit, TAP states of all free energies become marginally stable.Comment: Typos correcte

Landau gauge within the Gribov horizon

We consider a model which effectively restricts the functional integral of Yang--Mills theories to the fundamental modular region. Using algebraic arguments, we prove that this theory has the same divergences as ordinary Yang Mills theory in the Landau gauge and that it is unitary. The restriction of the functional integral is interpreted as a kind of spontaneous breakdown of the $BRS$ symmetry.Comment: 17 pages, NYU-TH-93/10/0

Explicit construction of the classical BRST charge for nonlinear algebras

We give an explicit formula for the Becchi-Rouet-Stora-Tyutin (BRST) charge associated with Poisson superalgebras. To this end, we split the master equation for the BRST charge into a pair of equations such that one of them is equivalent to the original one. We find the general solution to this equation. The solution possesses a graphical representation in terms of diagrams.Comment: 9 pages; v2,v3 minor corrections, references added for v

Renormalization of the N=1 Abelian Super-Chern-Simons Theory Coupled to Parity-Preserving Matter

We analyse the renormalizability of an Abelian N=1 super-Chern-Simons model coupled to parity-preserving matter on the light of the regularization independent algebraic method. The model shows to be stable under radiative corrections and to be gauge anomaly free.Comment: Latex, 7 pages, no figure

Renormalizations in softly broken N=1 theories: Slavnov-Taylor identities

Slavnov-Taylor identities have been applied to perform explicitly the renormalization procedure for the softly broken N=1 SYM. The result is in accordance with the previous results obtained at the level of supergraph technique.Comment: Latex, 17 pages, one statement about soft gauge beta function has been change

Abelian gauge theories on compact manifolds and the Gribov ambiguity

We study the quantization of abelian gauge theories of principal torus bundles over compact manifolds with and without boundary. It is shown that these gauge theories suffer from a Gribov ambiguity originating in the non-triviality of the bundle of connections whose geometrical structure will be analyzed in detail. Motivated by the stochastic quantization approach we propose a modified functional integral measure on the space of connections that takes the Gribov problem into account. This functional integral measure is used to calculate the partition function, the Greens functions and the field strength correlating functions in any dimension using the fact that the space of inequivalent connections itself admits the structure of a bundle over a finite dimensional torus. The Greens functions are shown to be affected by the non-trivial topology, giving rise to non-vanishing vacuum expectation values for the gauge fields.Comment: 33 page

The Several Guises of the BRST Symmetry

We present several forms in which the BRST transformations of QCD in covariant gauges can be cast. They can be non-local and even not manifestly covariant. These transformations may be obtained in the path integral formalism by non standard integrations in the ghost sector or by performing changes of ghost variables which leave the action and the path integral measure invariant. For different changes of ghost variables in the BRST and anti-BRST transformations these two transformations no longer anticommute.Comment: 3 pages, revte

Covariant scalar representation of iosp(d,2/2)iosp(d,2/2) quantization of the scalar relativistic particle

A covariant scalar representation of $iosp(d,2/2)$ is constructed and analysed in comparison with existing methods for the quantization of the scalar relativistic particle. It is found that, with appropriately defined wavefunctions, this $iosp(d,2/2)$ produced representation can be identified with the state space arising from the canonical BFV-BRST quantization of the modular invariant, unoriented scalar particle (or antiparticle) with admissible gauge fixing conditions. For this model, the cohomological determination of physical states can thus be obtained purely from the representation theory of the $iosp(d,2/2)$ algebra.Comment: 16 pages Late

Anomalous dimension of the gluon operator in pure Yang-Mills theory

We present new one loop calculations that confirm the theorems of Joglekar and Lee on the renormalization of composite operators. We do this by considering physical matrix elements with the operators inserted at non-zero momentum. The resulting IR singularities are regulated dimensionally. We show that the physical matrix element of the BRST exact gauge variant operator which appears in the energy- momentum tensor is zero. We then show that the physical matrix elements of the classical energy-momentum tensor and the gauge invariant twist two gluon operator are independent of the gauge fixing parameter. A Sudakov factor appears in the latter cases. The universality of this factor and the UV finiteness of the energy-momentum tensor provide another method of finding the anomalous dimension of the gluon operator. We conjecture that this method applies to higher loops and takes full advantage of the triangularity of the mixing matrix.Comment: submitted to Phys. Rev. D, 18 pages LaTEX uses psfig and revtex macros, figures appended as uuencoded Postscript file (complete Postsript version including figures available via anonymous ftp from ftp://max.physics.sunysb.edu/preprints/harris/paper.ps.Z), ITP-SB-94-3