Local Symmetries in the AdS_7/CFT_6 Correspondence

It is shown that local symmetry transformations of the maximal AdS supergravity in seven-dimensional anti de Sitter space induce those of the N=(2,0) conformal supergravity on the six-dimensional boundary at infinity. Boundary values of the AdS supergravity fields form a supermultiplet of the conformal supergravity.Comment: 13 pages, LaTe

PSU(2,2|4) transformations of IIB superstring in AdS_5 x S^5

The PSU(2,2|4) transformation laws of the IIB superstring theory in the AdS_5 x S^5 background are explicitly obtained for the light-cone gauge in the Green-Schwarz formalism.Comment: LaTeX, 14 pages, a reference adde

Gradient flows without blow-up for Lefschetz thimbles

We propose new gradient flows that define Lefschetz thimbles and do not blow up in a finite flow time. We study analytic properties of these gradient flows, and confirm them by numerical tests in simple examples.Comment: 31 pages, 11 figures, (v2) conclusion part is expande

Finite N Matrix Models of Noncommutative Gauge Theory

We describe a unitary matrix model which is constructed from discrete analogs of the usual projective modules over the noncommutative torus and use it to construct a lattice version of noncommutative gauge theory. The model is a discretization of the noncommutative gauge theories that arise from toroidal compactification of Matrix theory and it includes a recent proposal for a non-perturbative definition of noncommutative Yang-Mills theory in terms of twisted reduced models. The model is interpreted as a manifestly star-gauge invariant lattice formulation of noncommutative gauge theory, which reduces to ordinary Wilson lattice gauge theory for particular choices of parameters. It possesses a continuum limit which maintains both finite spacetime volume and finite noncommutativity scale. We show how the matrix model may be used for studying the properties of noncommutative gauge theory.Comment: 17 pp, Latex2e; Typos corrected, references adde

Liftable vector fields over corank one multigerms

In this paper, a systematic method is given to construct all liftable vector fields over an analytic multigerm $f: (\mathbb{K}^n, S)\to (\mathbb{K}^p,0)$ of corank at most one admitting a one-parameter stable unfolding.Comment: 34 pages. In ver. 2, several careless mistakes for calculations in Section 6 were correcte

Chiral anomalies in the reduced model

On the basis of an observation due to Kiskis, Narayanan and Neuberger, we show that there is a remnant of chiral anomalies in the reduced model when a Dirac operator which obeys the Ginsparg-Wilson relation is employed for the fermion sector. We consider fermions belonging to the fundamental representation of the gauge group U(N) or SU(N). For vector-like theories, we determine a general form of the axial anomaly or the topological charge within a framework of a U(1) embedding. For chiral gauge theories with the gauge group U(N), a remnant of gauge anomaly emerges as an obstruction to a smooth fermion integration measure. The pure gauge action of gauge-field configurations which cause these non-trivial phenomena always diverges in the 't Hooft $N\to\infty$ limit when d>2.Comment: 20 pages, uses JHEP.cls and amsfonts.sty, the final version to appear in JHE

Three-Form Flux with N=2 Supersymmetry on AdS_5 x S^5

In the context of the AdS/CFT correspondence the general form of a three-form flux perturbation to the AdS_5 x S^5 solution in the type IIB supergravity which preserves N=2 supersymmetry is obtained. The arbitrary holomorphic function appearing in the N=1 case studied by Grana and Polchinski is restricted to a quadratic function of the coordinates transverse to the D3-branes.Comment: 11 pages, LaTe