We reopen the discussion of gauging two-dimensional off-shell (2,2) supersymmetric sigma models written in terms of semichiral superfields. The gauging is now done by coupling the semichiral superfields to the new (2,2) semichiral vector multiplet. We show that the two moment maps together with a third function form the complete set of three Killing potentials which are associated with this gauging. These Killing potentials lead to generalized moment maps. Next we construct the T-duality map, while keeping (2,2) supersymmetry manifest. In the T-dual description, a pair of left and right semichiral superfields is replaced by a pair of chiral and twisted chiral multiplets. We end with a discussion on quotient construction.

We calculate the most general causal N = 1 three-dimensional, gauge invariant action coupled to matter in superspace and derive its component form using Ectoplasmic integration theory. One example of such an action can be obtained by compactifying M-theory on a Spin(7) holonomy manifold taking non-vanishing fluxes into account. We show that the resulting three-dimensional theory is in agreement with the more general construction. The scalar potential resulting from Kaluza-Klein compactification stabilizes all the moduli fields describing deformations of the metric except for the radial modulus. This potential can be written in terms of the superpotential previously discussed in the literature. melanieb@physics.umd.edu, dragos@physics.umd.edu, gatess@wam.umd.edu, ldw@physics.umd.edu, williem@physics.umd.edu, ferrigno@physics.umd.edu

Title of dissertation: APPLICATIONS OF SUPERSPACE TECHNIQUES TO EFFECTIVE ACTIONS, COMPLEX GEOMETRY, AND T DUALITY IN STRING THEORY Willie Carl Merrell II Doctor of Philosophy, 2007 Dissertation directed by: Professor S. James Gates, Jr. Department of Physics We describe the use of superspace techniques to discuss some of the issues in string theory. First we use superspace techniques to derive the effective action for the 10D N = 1 Heterotic string perturbatively to first order in the parameter α′. Next we demonstrate how to use the superspace description of the supersymmetric gauge multiplet for chiral superfield in 2d N = (2, 2) to discuss T duality for sigma models that realizes a particular case of generalized Kahler geometry. We find that the salient features of T duality are captured but at the cost of introducing unwanted fields in dual sigma model. Fortunately the extra fields decouple from the relevant fields under consideration. This leads us to introduce a new supersymmetric gauge multiplet that will eliminate the need to introduce extra fields in the dual sigma model. APPLICATIONS OF SUPERSPACE TECHNIQUES TO EFFECTIVE ACTIONS COMPLEX GEOMETRY, AND T DUALITY IN STRING THEORY by Willie Carl Merrell II Dissertation submitted to the Faculty of the Graduate School of the University of Maryland, College Park in partial fulfillment of the requirements for the degree of Doctor of Philosophy 2007 Advisory Committee: Professor S. James Gates, Jr., Chair/Advisor Professor Thomas D. Cohen Professor Theodore A. Jacobson Professor Markus A. Luty Professor Jonathan Rosenberg

We gauge the (2, 2) supersymmetric non-linear sigma model whose target space has bihermitian structure (g, B, J±) with noncommuting complex structures. The bihermitian geometry is realized by a sigma model which is written in terms of (2, 2) semi-chiral superfields. We discuss the moment map, from the perspective of the gauged sigma model action and from the integrability condition for a Hamiltonian vector field. We show that for a concrete example, the SU(2) × U(1) WZNW model, as well as for the sigma models with almost product structure, the moment map can be used together with the corresponding Killing vector to form an element of T⊕T* which lies in the eigenbundle of the generalized almost complex structure. Lastly, we discuss T-duality at the level of a (2,2) sigma model involving semi-chiral superfields and present an explicit example.

We describe a new 1 + 1 dimensional N = (2, 2) vector multiplet that naturally couples to semi chiral superfields in the sense that the gauged supercovariant derivative algebra is only consistent with imposing covariantly semi chiral superfield constraints.It has the advantages that its prepotentials shift by semi chiral superfields under gauge transformations.We also see that the multiplet relates the chiral vector multiplet with the twisted chiral vector multiplet by reducing to either multiplet under appropriate limits without being reducible in terms of the chiral and twisted chiral vector multiplet.This is explained from the superspace geometrical point of view as the result of possessing a symmetry under the discrete supercoordinate transformation that is responsible for mirror copies of supermultiplets.We then describe how to gauge a non linear sigma model with semi chiral superfields using the prepotentials of the new multiplet.

We describe a new 1 + 1 dimensional = (2, 2) vector multiplet that naturally couples to semi chiral superfields in the sense that the gauged supercovariant derivative algebra is only consistent with imposing covariantly semi chiral superfield constraints. It has the advantage that its prepotentials shift by semi chiral superfields under gauge transformations. We also see that the multiplet relates the chiral vector multiplet with the twisted chiral vector multiplet by reducing to either multiplet under appropriate limits without being reducible in terms of the chiral and twisted chiral vector multiplet. This is explained from the superspace geometrical point of view as the result of possessing a symmetry under the discrete supercoordinate transformation that is responsible for mirror copies of supermultiplets. We then describe how to gauge a non linear sigma model with semi chiral superfields using the prepotentials of the new multiplet.

We calculate the most general causal N=1 three-dimensional, gauge invariant action coupled to matter in superspace and derive its component form using Ectoplasmic integration theory. One example of such an action can be obtained by compactifying M-theory on a Spin(7) holonomy manifold taking non-vanishing fluxes into account. We show that the resulting three-dimensional theory is in agreement with the more general construction. The scalar potential resulting from Kaluza-Klein compactification stabilizes all the moduli fields describing deformations of the metric except for the radial modulus. This potential can be written in terms of the superpotential previously discussed in the literature.

Utilizing a first-order perturbative superspace approach, we derive the bosonic equations of motion for the 10D, N = 1 supergravity fields. We give the lagrangian corresponding to these equations derived from superspace geometry. Moreover, the equivalence of this lagrangian to the first-order perturbative component level lagrangian of anomaly-free supergravity is proven. Our treatment covers both the two-form and six-form formulations.