Topics in Gauge/Gravity Duality

Includes bibliographical references.The gauge theory/gravity correspondence encompasses a variety of di_erent specific dualities. We investigate various topics in the context of Super–Yang- Mills/type IIB string theory and superconformal Chern-Simons-matter/type IIA string theory dualities. We carry out a rather extensive study of the type IIA AdS3_S3_S3_S1 Green- Schwarz superstring, up to quadratic order in fermions. We discuss issues related to fixing its _-symmetry and show the one-loop finiteness of two-point functions of bosonic fields. We then perform a Hamiltonian analysis and compare SU(2) string states with predictions from the conjectured Bethe equations. Furthermore, we show that, at least at tree-level, the two-body S-matrix is reflectionless. We then concern ourselves with extending Mikhailov’s construction of giant gravitons from holomorphic functions to include meromorphic functions, which lead to giants with non-trivial topologies in AdS5_S5. We explore what topological configurations giants, whose dynamics preserve a certain amount of supersymmetry, assume. We are particularly interested in solutions created by a localised modification of a set of intersecting spherical giant gravitons, as this seems the most tractable limit. We finally explore some aspects of holographic particle-vortex duality, in particular its realisation in the ABJM model and a possible relation to Maxwell duality in AdS4. We formulate a symmetric version of the transformation that acts as a self-duality, show how to embed it as an abelian duality in the (2+1)-dimensional, N = 6 super–Chern-Simons-matter theory that is the ABJM model, and speculate on a possible non-abelian extension

Meromorphic Functions and the Topology of Giant Gravitons

Using Mikhailov's map from holomorphic functions to supersymmetric D3-brane solutions, we show how to construct giant gravitons in AdS5 x S5 with toroidal topologies. In the 1/4-BPS sector we show that these are always of the form #^K (S2 x S1), and in the limit in which this becomes a set of m+n perpendicular spherical giants re-connected near to their intersections, we find K in terms of m,n. In the 1/8-BPS sector we find a similar class of solutions.Comment: 10 pages, 8 figure

Particle-vortex and Maxwell duality in the AdS4×CP3AdS_4\times \mathbb{CP}^3/ABJM correspondence

We revisit the notion of particle-vortex duality in abelian theories of complex scalar fields coupled to gauge fields, formulating the duality as a transformation at the level of the path integral. This transformation is then made symmetric and cast as a self-duality that maps the original theory into itself with the role of particles and vortices interchanged. After defining the transformation for a pure Chern-Simons gauge theory, we show how to embed it into (a sector of) the $(2+1)-$dimensional ABJM model, and argue that this duality can be understood as being related to 4-dimensional Maxwell duality in the $AdS_{4}\times\mathbb{CP}^{3}$ bulk.Comment: 29 page

Near BMN dynamics of the AdS(3) x S(3) x S(3) x S(1) superstring

We investigate the type IIA AdS(3) x S(3) x M(4) superstring with M(4)=S(3) x S(1) or M(4)=T(4). String theory in this background is interesting because of AdS3/CFT2 and its newly discovered integrable structures. We derive the kappa symmetry gauge-fixed Green-Schwarz string action to quadratic order in fermions and quartic order in fields utilizing a near BMN expansion. As a first consistency check of our results we show that the two point functions are one-loop finite in dimensional regularization. We then perform a Hamiltonian analysis where we compare the energy of string states with the predictions of a set of conjectured Bethe equations. While we find perfect agreement for single rank one sectors, we find that the product SU(2) x SU(2) sector does not match unless the Bethe equations decouple completely. We then calculate 2 to 2 bosonic tree-level scattering processes on the string worldsheet and show that the two-dimensional S-matrix is reflectionless. This might be important due to the presence of massless worldsheet excitations which are generally not described by the Bethe equations.Comment: 28 pages; v2: Fixed signs and eq. (B.1), results unchanged, one reference added; v3: Matches published versio