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We study the quantum dynamics of a system of n Abelian N = 1 vector multiplets coupled to 1 2 n n + 1 chiral multiplets which parametrise the Hermitian symmetric space Sp(2n, ℝ)/U(n). In the presence of supergravity, this model is super-Weyl invariant and possesses the maximal non-compact duality group Sp(2n, ℝ) at the classical level. These symmetries should be respected by the logarithmically divergent term (the "induced action") of the effective action obtained by integrating out the vector multiplets. In computing the effective action, one has to deal with non-minimal operators for which the known heat kernel techniques are not directly applicable, even in flat (super)space. In this paper we develop a method to compute the induced action in Minkowski superspace. The induced action is derived in closed form and has a simple structure. It is a higher-derivative superconformal sigma model on Sp(2n, ℝ)/U(n). The obtained N = 1 results are generalised to the case of N = 2 local supersymmetry: a system of n Abelian N = 2 vector multiplets coupled to N = 2 chiral multiplets XI parametrising Sp(2n, ℝ)/U(n). The induced action is shown to be proportional to ∫ d 4 x d 4 θ d 4 θ ¯ E K X X ¯ , where K X X ¯ is the Kähler potential for Sp(2n, ℝ)/U(n). We also apply our method to compute DeWitt's a2 coefficients in some non-supersymmetric theories with non-minimal operators. [ABSTRACT FROM AUTHOR]

We review the matter induced part of the effective superpotential of $\mathcal{N} = 2$, U(N) gauge model in which $\mathcal{N} = 2$ supersymmetry is spontaneously broken to $\mathcal{N} = 1$. We derive this by the diagrammatical computation and by using the properties of the chiral ring and the generalized Konishi anomaly equations. [ABSTRACT FROM AUTHOR]

We derive the master function governing the component action of the four-dimensional nonanticommutative (NAC) and fully N = 2 supersymmetric gauge field theory with a nonsimple gauge group U(2) = SU(2) × U(1). The new NAC master function is a nontrivial generalization of the known master functions in the NAC, N = 2 supersymmetric gauge theories with the U(1) and SU(2) gauge groups. We use a Lorentz-singlet NAC-deformation parameter and an N = 2 supersymmetric star (Moyal) product, which do not break any of the fundamental symmetries of the undeformed N = 2 gauge theory. The scalar potential in the NAC-deformed theory is calculated. We also propose the non-Abelian BPS-type equations in the case of the NAC-deformed N = 2 gauge theory with the SU(2) gauge group, and comment on the SU(3) case too. The NAC-deformed field theories can be thought of as the effective (nonperturbative) N = 2 gauge field theories in a certain (scalar only) N = 2 supergravity background. [ABSTRACT FROM AUTHOR]

We study five-dimensional superconformal field theories and their holographic dual, matter-coupled Romans supergravity. On the one hand, some recently derived formulae allow us to extract the central charges from deformations of the supersymmetric five-sphere partition function, whose large N expansion can be computed using matrix model techniques. On the other hand, the conformal and flavor central charges can be extracted from the six-dimensional supergravity action, by carefully analyzing its embedding into type I’ string theory. The results match on the two sides of the holographic duality. Our results also provide analytic evidence for the symmetry enhancement in five-dimensional superconformal field theories. [ABSTRACT FROM AUTHOR]

We address the question of determining the prepotential of the gauged supergravity resulting from a compactification of M-theory on AdS4 × Y7. We make a concrete proposal for the prepotential in the case of toric Sasaki-Einstein Y7. Comparison with direct Kaluza-Klein computations show that the proposal is correct in certain cases, but requires modification in general. [ABSTRACT FROM AUTHOR]