Integrating Over Higgs Branches

We develop some useful techinques for integrating over Higgs branches in supersymmetric theories with 4 and 8 supercharges. In particular, we define a regularized volume for hyperkahler quotients. We evaluate this volume for certain ALE and ALF spaces in terms of the hyperkahler periods. We also reduce these volumes for a large class of hyperkahler quotients to simpler integrals. These quotients include complex coadjoint orbits, instanton moduli spaces on R^4 and ALE manifolds, Hitchin spaces, and moduli spaces of parabolic Higgs bundles on Riemann surfaces. In the case of Hitchin spaces the evaluation of the volume reduces to a summation over solutions of Bethe Ansatz equations for the non-linear Schroedinger system. We discuss some applications of our results.Comment: 32pp. harvmac big mode; v.2 34pp. typos fixed, sections 4.1, 5.2 substantially improve

D-particle bound states and generalized instantons

We compute the principal contribution to the index in the supersymmetric quantum mechanical systems which are obtained by reduction to 0+1 dimensions of $\mathcal{N}=1$, $D=4,6,10$ super-Yang-Mills theories with gauge group SU(N). The results are: ${1\over{N^{2}}}$ for $D=4,6$, $\sum_{d | N} {1\over{d^{2}}}$ for D=10. We also discuss the D=3 case.Comment: harvmac, 24 pages; v2. references added, typos corrected; v3. one more reference adde

Generalized Conifolds and 4d N=1 SCFT

This paper lays groundwork for the detailed study of the non-trivial renormalization group flow connecting supersymmetric fixed points in four dimensions using string theory on AdS spaces. Specifically, we consider D3-branes placed at singularities of Calabi-Yau threefolds which generalize the conifold singularity and have an ADE classification. The $\mathcal{N}=1$ superconformal theories dictating their low-energy dynamics are infrared fixed points arising from deforming the corresponding ADE $\mathcal{N}=2$ superconformal field theories by mass terms for adjoint chiral fields. We probe the geometry with a single $D3$-brane and discuss the near-horizon supergravity solution for a large number $N$ of coincident $D3$-branes.Comment: harvmac 27pp; v2. refs added, typos corrected, abstract renormalized, v3. more of that sort, version to appear in JHE

Towards Integrability of Topological Strings I: Three-forms on Calabi-Yau manifolds

The precise relation between Kodaira-Spencer path integral and a particular wave function in seven dimensional quadratic field theory is established. The special properties of three-forms in 6d, as well as Hitchin's action functional, play an important role. The latter defines a quantum field theory similar to Polyakov's formulation of 2d gravity; the curious analogy with world-sheet action of bosonic string is also pointed out.Comment: 31 page

Darboux coordinates, Yang-Yang functional, and gauge theory

The moduli space of SL(2) flat connections on a punctured Riemann surface with the fixed conjugacy classes of the monodromies around the punctures is endowed with a system of holomorphic Darboux coordinates, in which the generating function of the variety of SL(2)-opers is identified with the universal part of the effective twisted superpotential of the corresponding four dimensional N=2 supersymmetric theory subject to the two-dimensional Omega-deformation. This allows to give a definition of the Yang-Yang functionals for the quantum Hitchin system in terms of the classical geometry of the moduli space of local systems for the dual gauge group, and connect it to the instanton counting of the four dimensional gauge theories, in the rank one case.Comment: 25 pages, 11 figures, v1. in the proceedings of Cargese conference "String Theory: Formal Developments and Applications" (Jun 21-Jul 3, 2010); reported also at six other conferences in 2010, v2. references correcte

Issues in Topological Gauge Theory

We discuss topological theories, arising from the general $\mathcal{N}=2$ twisted gauge theories. We initiate a program of their study in the Gromov-Witten paradigm. We re-examine the low-energy effective abelian theory in the presence of sources and study the mixing between the various $p$-observables. We present the twisted superfield formalism which makes duality transformations transparent. We propose a scheme which uniquely fixes all the contact terms. We derive a formula for the correlation functions of $p$-observables on the manifolds of generalized simple type for $0 \leq p \leq 4$ and on some manifolds with $b_{2}^{+} =1$. We study the theories with matter and explore the properties of universal instanton. We also discuss the compactifications of higher dimensional theories. Some relations to sigma models of type $A$ and $B$ are pointed out and exploited.Comment: 72 pp., Harvmac (b) mode, some typos corrected, reference adde

Metamorphosis Of Tachyon Profile In Unstable D9-Branes

We explored a variety of brane configurations in our previous paper within the two derivative truncation of the unstable D9-brane effective theory. In this paper we extend our previous results with emphasis on the inclusion of the higher derivative corrections for the tachyon and the gauge fields computed in the boundary string field theories. We give the exact solutions to BPS brane configurations studied in our previous paper and find remarkable exact agreements of their energies and RR-charges with the expected results. We further find a few more solutions that we could not construct in the two derivative truncations, such as a (F,D6) bound state ending on a D8-brane whose existence turns out to be due to a higher derivative effect and also the dielectric brane of Emparan and Myers as a nonsupersymmetric example. These are also in exact agreements with the results obtained in the effective theory of supersymmetric D-branes.Comment: 26 pages, LaTeX, (v2) minor corrections and a misleading footnote concerning the paper hep-th/0012198 was eliminated. References added, (v3) an important correction of the normalizations in the action, while the results being intac