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Register a new userA New Class of N=2 Topological Amplitudes
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We describe a new class of N=2 topological amplitudes that compute a particular class of BPS terms in the low energy effective supergravity action. Specifically they compute the coupling F^2(lambdalambda)^{g-2}(dphi)^2 where F, lambda and phi are gauge field strengths, gaugino and holomorphic vector multiplet scalars. The novel feature of these terms is that they depend both on the vector and hypermultiplet moduli. The BPS nature of these terms implies that they satisfy a holomorphicity condition with respect to vector moduli and a harmonicity condition as well as a second order differential equation with respect to hypermultiplet moduli. We study these conditions explicitly in heterotic string theory and show that they are indeed satisfied up to anomalous boundary terms in the world-sheet moduli space. We also analyze the boundary terms in the holomorphicity and harmonicity equations at a generic point in the vector and hyper moduli space. In particular we show that the obstruction to the holomorphicity arises from the one loop threshold correction to the gauge couplings and we argue that this is due to the contribution of non-holomorphic couplings to the connected graphs via elimination of the auxiliary fields.
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In arXiv:0905.3629 we described a new class of N=2 topological amplitudes that depends both on vector and hypermultiplet moduli. Here we find that this class is actually a particular case of much more general topological amplitudes which appear at higher loops in heterotic string theory compactified on K3 x T^2. We analyze their effective field theory interpretation and derive particular (first order) differential equations as a consequence of supersymmetry Ward identities and the 1/2-BPS nature of the corresponding effective action terms. In string theory the latter get modified due to anomalous world-sheet boundary contributions, generalizing in a non-trivial way the familiar holomorphic and harmonicity anomalies studied in the past. We prove by direct computation that the subclass of topological amplitudes studied in arXiv:0905.3629 forms a closed set under these anomaly equations and that these equations are integrable.
We introduce two new N = (2, 2) vector multiplets that couple naturally to generalized Kahler geometries. We describe their kinetic actions as well as their matter couplings both in N = (2, 2) and N = (1, 1) superspace.
We construct several novel examples of 3d $mathcal{N}=2$ models whose free energy scales as $N^{3/2}$ at large $N$. This is the first step towards the identification of field theories with an M-theory dual. Furthermore, we match the volumes extracted from the free energy with the ones computed from the Hilbert series. We perform a similar analysis for the 4d parents of the 3d models, matching the volume extracted from the $a$ conformal anomaly to that obtained from the Hilbert series. For some of the 4d models, we show the existence of a Sasaki-Einstein metric on the internal space of the candidate type IIB gravity dual.
Using four-dimensional unitarity and MHV-rules we calculate the one-loop MHV amplitudes with all external particles in the adjoint representation for N=2 supersymmetric QCD with N_f fundamental flavours. We start by considering such amplitudes in the superconformal N=4 gauge theory where the N=4 supersymmetric Ward identities (SWI) guarantee that all MHV amplitudes for all types of external particles are given by the corresponding tree-level result times a universal helicity- and particle-type-independent contribution. In N=2 SQCD the MHV amplitudes differ from those for N=4 for general values of N_f and N_c. However, for N_f=2N_c where the N=2 SQCD is conformal, the N=2 MHV amplitudes (with all external particles in the adjoint representation) are identical to the N=4results. This factorisation at one-loop motivates us to pose a question if there may be a BDS-like factorisation for these amplitudes which also holds at higher orders of perturbation theory in superconformal N=2 theory.
We propose new off-shell models for spontaneously broken local ${cal N}=2$ supersymmetry, in which the supergravity multiplet couples to nilpotent Goldstino superfields that contain either a gauge one-form or a gauge two-form in addition to spin-1/2 Goldstone fermions and auxiliary fields. In the case of ${cal N}=2$ Poincare supersymmetry, we elaborate on the concept of twisted chiral superfields and present a nilpotent ${cal N}=2$ superfield that underlies the cubic nilpotency conditions given in arXiv:1707.03414 in terms of constrained ${cal N}=1$ superfields.
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