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We study field models for which a quantum action (i.e. the action appearing in the generating functional of Green functions) is invariant under supersymmetric transformations. We derive the Ward identity which is direct consequence of this invariance. We consider a change of variables in functional integral connected with supersymmetric transformations when its parameter is replaced by a nilpotent functional of fields. Exact form of the corresponding Jacobian is found. We find restrictions on generators of supersymmetric transformations when a consistent quantum description of given field theories exists.
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The recent developments in fluid/gravity correspondence give a new impulse to the study of fluid dynamics of supersymmetric theories. In that respect, the entropy current formalism requires some modifications in order to be adapted to supersymmetric theories and supergravities. We formulate a new entropy current in superspace with the properties: 1) it is conserved off-shell for non dissipative fluids, 2) it is invariant under rigid supersymmetry transformations 3) it is covariantly closed in local supersymmetric theories 4) it reduces to its bosonic expression on space-time.
We analyse the relation between anomalies in their manifestly supersymmetric formulation in superspace and their formulation in Wess-Zumino (WZ) gauges. We show that there is a one-to-one correspondence between the solutions of the cohomology problem in the two formulations and that they are related by a particular choice of a superspace counterterm (scheme). Any apparent violation of $Q$-supersymmetry is due to an explicit violation by the counterterm which defines the scheme equivalent to the WZ gauge. It is therefore removable.
In this talk I review some recent results concerning multi-instanton calculus in supersymmetric field theories. More in detail, I will show how these computations can be efficiently performed using the formalism of topological field theories.
Seiberg-Witten solutions of four-dimensional supersymmetric gauge theories possess rich but involved integrable structures. The goal of this paper is to show that an isomonodromy problem provides a unified framework for understanding those various features of integrability. The Seiberg-Witten solution itself can be interpreted as a WKB limit of this isomonodromy problem. The origin of underlying Whitham dynamics (adiabatic deformation of an isospectral problem), too, can be similarly explained by a more refined asymptotic method (multiscale analysis). The case of $N=2$ SU($s$) supersymmetric Yang-Mills theory without matter is considered in detail for illustration. The isomonodromy problem in this case is closely related to the third Painleve equation and its multicomponent analogues. An implicit relation to $ttbar$ fusion of topological sigma models is thereby expected.
We study the duality cascade of softly broken supersymmetric theories. We investigate the renormalization group (RG) flow of SUSY breaking terms as well as supersymmetric couplings. It is found that the magnitudes of SUSY breaking terms are suppressed in most regimes of the RG flow through the duality cascade. At one stage of cascading, the gaugino mass of the strongly coupled sector and scalar masses converge to certain values, which are determined by the gauge coupling and the gaugino mass of the weakly coupled sector. At the next stage, the strongly and weakly coupled sectors are interchanged with each other. We also show the possibility that cascading would be terminated by the gauge symmetry breaking, which is induced by the so-called B-term.
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