arXiv subjects
Publications and source records attributed to M. Rocek.
We consider theories with degenerate kinetic terms such as those that arise at strong coupling in $N=2$ super Yang-Mills theory. We compute the components of generalized $N=1,2$ supersymmetric sigma model actions in two dimensions. The target space coordinates may be matter and/or Yang-Mills superfield strengths.
We discuss the conditions for extra supersymmetry of the N=(2,2) supersymmetric vector multiplets described in arXiv:0705.3201 [hep-th] and in arXiv:0808.1535 [hep-th]. We find (4,4) supersymmetry for the semichiral vector multiplet but not for the Large Vector Multiplet.
We describe the conditions for extra supersymmetry in N=(2,2) supersymmetric nonlinear sigma models written in terms of semichiral superfields. We find that some of these models have additional off-shell supersymmetry. The (4,4) supersymmetry introduces geometrical structures on the target-space which are conveniently described in terms of Yano f-structures and Magri-Morosi concomitants. On-shell, we relate the new structures to the known bi-hypercomplex structures.
The projective superspace formulation for four-dimensional N = 2 matter-coupled supergravity presented in arXiv:0805.4683 makes use of the variant superspace realization for the N = 2 Weyl multiplet in which the structure group is SL(2,C) x SU(2) and the super-Weyl transformations are generated by a covariantly chiral parameter. An extension to Howe's realization of N = 2 conformal supergravity in which the tangent space group is SL(2,C) x U(2) and the super-Weyl transformations are generated by a real unconstrained parameter was briefly sketched. Here we give the explicit details of the extension.
This paper presents a projective superspace formulation for 4D N = 2 matter-coupled supergravity. We first describe a variant superspace realization for the N = 2 Weyl multiplet. It differs from that proposed by Howe in 1982 by the choice of the structure group (SO(3,1) x SU(2) versus SO(3,1) x U(2)), which implies that the super-Weyl transformations are generated by a covariantly chiral parameter instead of a real unconstrained one. We introduce various off-shell supermultiplets which are curved superspace analogues of the superconformal projective multiplets in global supersymmetry and which describe matter fields coupled to supergravity. A manifestly locally supersymmetric and super-Weyl invariant action principle is given. Off-shell locally supersymmetric nonlinear sigma models are presented in this new superspace.
We show that the connection between partial breaking of supersymmetry and nonlinear actions is not accidental and has to do with constraints that lead directly to nonlinear actions of the Born-Infeld type. We develop a constrained superfield approach that gives a universal way of deriving and using these actions. In particular, we find the manifestly supersymmetric form of the action of the 3-brane in 6-dimensional space in terms of N=1 superfields by using the tensor multiplet as a tool. We explain the relation between the Born-Infeld action and the model of partial N=2 supersymmetry breaking by a dual D-term. We represent the Born-Infeld action in a novel form quadratic in the gauge field strengths by introducing two auxiliary complex scalar fields; this makes duality covariance and the connection with the N=1 supersymmetric extension of the action very transparent. We also suggest a general procedure for deriving manifestly duality symmetric actions, explaining in a systematic way relations between previously discussed Lorentz covariant and noncovariant actions.
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We find the N-soliton solution at infinite theta, as well as the metric on the moduli space corresponding to spatial displacements of the solitons. We use a perturbative expansion to incorporate the leading 1/theta corrections, and find an effective short range attraction between solitons. We study the stability of various solutions. We discuss the finite theta corrections to scattering, and find metastable orbits. Upon quantization of the two-soliton moduli space, for any finite theta, we find an s-wave bound state.
We show that the Higgs branch of a four-dimensional Yang-Mills theory, with gauge and matter content summarised by an ADE quiver diagram, is identical to the generalised Coulomb branch of a four-dimensional superconformal strongly coupled gauge theory with ADE global symmetry. This equivalence suggests the existence of a mirror symmetry between the quiver theories and the strongly coupled theories.
The full low energy effective action of N=4 SYM is believed to be self-dual. Starting with the first two leading terms in a momentum expansion of this effective action, we perform a duality transformation and find the conditions for self-duality. These determine some of the higher order terms. We compare the effective action of N=4 SYM with the probe-source description of type II_B D3-branes in the AdS_5 \times S_5 background. We find agreement up to six derivative terms if we identify the separation of the 3-branes with a redefinition of the gauge scalar that involves the gauge field strength.
Beginning with the Legendre transform construction of hyperkähler metrics, we analyze the ALF version of the D_n metrics. We determine the constraint equation obtained from extremizing the $w$ coordinate of the generating function F(z,\bar{z},u,\bar{u},w) and study its behavior as we send two of the mass parameters of the $D_n$ metric to zero. We find that the constraint equation enforces the limit that the metric becomes that of multi-Taub-NUT.
The N=1 superspace generalization of the 3-brane action in 6 dimensions with partially broken N=2 supersymmetry can be constructed using N=1 chiral, complex linear, or real linear superfields. The physical scalars of these multiplets give equivalent descriptions of the two transverse coordinates. The second supersymmetry is realized nonlinearly in all these actions. We derive the superspace brane actions and their nonlinear supersymmetry for both kinds of linear superfields when we break N=2 supersymmetry spontaneously. This breaking is realized in the free action of hypermultiplets that live in N=2 projective superspace by constraining the N=2 multiplets to reduce them to a pure Goldstone multiplet. For the chiral superfield, the superspace brane action and nonlinear supersymmetry can be deduced by dualizing the brane action of either linear superfield. We find that the dual action is unique up to field redefinitions that introduce arbitrariness in the dependence on the auxiliary fields.
The effective action of N=2 gauge multiplets in general includes higher-dimension UV finite nonholomorphic corrections integrated with the full N=2 superspace measure. By adding a hypermultiplet in the adjoint representation we study the effective action of N=4 SYM. The nonanomalous SU(4) R-symmetry of the classical N=4 theory must be also present in the on-shell effective action, and therefore we expect to find similar nonholomorphic terms for each of the scalars in the hypermultiplet. The N=2 path integral quantization formalism developed in projective superspace allows us to compute these hypermultiplet nonholomorphic terms directly in N=2 superspace. The corresponding gauge multiplet expression can be successfully compared with the result inferred from a N=1 calculation in the abelian subsector.
Manifestly N=2 supersymmetric Feynman rules are found for different off-shell realizations of the massless hypermultiplet in projective superspace. When we reduce the Feynman rules to an N=1 superspace we obtain the correct component propagators. The Feynman rules are shown to be compatible with a ``duality'' that acts only on the auxiliary fields, as well as with the usual duality relating the hypermultiplet to the tensor multiplet.
We have carried out a two loop computation of the low-energy effective action for the four-dimensional N=2 supersymmetric Yang-Mills system coupled to hypermultiplets, with the chiral superfields of the vector multiplet lying in an abelian subalgebra. We have found a complete cancellation at the level of the integrands of Feynman amplitudes, and therefore the two loop contribution to the action, effective or Wilson, is identically zero.
We present a new 4D, N = 1 supersymmetric nonlinear sigma-model using complex linear and chiral superfields that generalizes the massless limit of the QCD effective action of Gasser and Leutwyler.
We propose a Wilsonian action compatible with special geometry and higher dimension N=2 corrections, and show that the holomorphic contribution F to the low energy effective action is independent of the infrared cutoff. We further show that for asymptotically free SU(2) super Yang-Mills theories, the infrared cutoff can be tuned to cancel leading corrections to F. We also classify all local higher-dimensional contributions to the N=2 superspace effective action that produce corrections to the Kahler potential when reduced to N=1 superspace.
We compute the $1$-loop effective Kähler potential in the most general renormalizable $N=1$ $d=4$ supersymmetric quantum field theory.