J. Rahmfeld

Near horizon superspace

The adSp+2 × Sd−p−2 geometry of the near horizon branes is promoted to a supergeometry: the solution of the supergravity constraints for the vielbein, connection and form superfields are found. This supergeometry can be used for the construction of new superconformal theories. We also discuss the Green-Schwarz action for a type IIB string on adS5 × S5.

The GS string action on AdS5×S5

Abstract We present a simple form of the Type IIB string action on AdS 5 × S 5 . The result is achieved by fixing κ -symmetry in the Killing spinor gauge defined by the projector of the Killing spinor of the D3 brane. We show explicitly that in this gauge the superspace is greatly simplified which is the crucial ingredient for the simple string action.

Supertwistors as quarks of SU(2,2|4)

The GS superstring on AdS5 × S5 has a nonlinearly realized, spontaneously broken SU(2,2|4) symmetry. Here we introduce a two-dimensional model in which the unbroken SU(2,2|4) symmetry is linearly realized. The basic variables are supertwistors, which transform in the fundamental representation of this supergroup. The quantization of this supertwistor model leads to the complete oscillator construction of the unitary irreducible representations of the centrally extended SU(2,2|4). They include the states of d = 4 SYM theory, massless and KK states of AdS5 supergravity, and the descendants on AdS5 of the standard massive string states, which form intermediate and long massive supermultiplets. We present examples of long massive supermultiplets and discuss possible states of solitonic and (p,q) strings.

Green-Schwarz string action on AdS 3 × S 3 with Ramond-Ramond charge

We derive the classical kappa-symmetric Type IIB string action on AdS(3) x S(3) by employing the SU(1,1|2)^2 algebra. We then gauge fix kappa-symmetry in the background adapted Killing spinor gauge and present the action in a very simple form.

BPS spectrum of 5 dimensional field theories, (p,q) webs and curve counting

We study the BPS spectrum of supersymmetric 5 dimensional field theories and their representations as string webs. It is found that a state of given charges exists when it has a representation as an irreducible string web. Its spin is determined by the string web. The number of fermionic zero modes is 8g+4b, where g is the number of internal faces and b is the number of boundaries. In the lift to M theory of 4d field theories such states are described by membranes ending on the 5-brane, breaking SUSY from 8 to 4, and g becomes the genus of the membrane. Mathematically, we obtain a diagrammatic method to find the spectrum of curves on a toric complex surface, and the number of their moduli.

The GS string action on AdS(3) x S(3) with Ramond-Ramond charge

We derive the classical kappa-symmetric Type IIB string action on AdS(3) x S(3) by employing the SU(1,1|2)^2 algebra. We then gauge fix kappa-symmetry in the background adapted Killing spinor gauge and present the action in a very simple form.

A SIMPLE PARTICLE ACTION FROM A TWISTOR PARAMETRIZATION OF ADS5

Abstract The SO (4,2) isometries of AdS 5 are realized non-linearly on its horospherical coordinates ( x m , ρ ). On the other hand, Penrose twistors have long been known to linearly realize these symmetries on 4-dimensional Minkowski space, the boundary of AdS 5 , parametrized by x m . Here we extend the twistor construction and define a pair of twistors, allowing us to include a radial coordinate in the construction. The linear action of SO (4,2) on the twistors induces the correct isometries of AdS 5 . We apply this new construction to the study of the dynamics of a massive particle in AdS 5 . We show that in terms of the twistor variables the action takes a simple form of a 1-dimensional gauge theory. Our result might open up the possibility to find a simple worldvolume action also for the string propagating on AdS 5 .

Symmetries of the boundary of AdS5 × S5 and harmonic superspace

We study the boundary limit of the bulk isometries of AdS × S. The superconformal symmetry is realized on the coordinates of the AdS boundary, the fermionic superspace coordinates, and the harmonics on the sphere. We show how these may be related to the coordinates of an off-shell harmonic superspace of SCFT living on the boundary. In the special case of d = 4, = 2 super Yang-Mills theory, a truncation of the = 4 SYM dual to type-IIB string theory compactified on AdS5 × S5, we identify the bosonic space SU(2)/U(1) of the = 2 harmonic superspace (known before as auxiliary) with the S2 submanifold of the S5.

One loop supergravity corrections to the black hole entropy and residual supersymmetry

We study the one-loop corrections to the effective on-shell action of N=2 supergravity in the background of the Reissner-Nordstrom black hole. In the extreme case the contributions from graviton, gravitino and photon to the one-loop corrections to the entropy are shown to cancel. This gives the first explicit example of the supersymmetric non-renormalization theorem for the on-shell action (entropy) for BPS configurations which admit Killing spinors. We display the residual supersymmetry of the perturbations of a general supersymmetric theory in a bosonic BPS background.

Green-Schwarz string action on AdS[sub 3][times]S[sup 3] with Ramond-Ramond charge

We derive the classical kappa-symmetric Type IIB string action on AdS(3) x S(3) by employing the SU(1,1|2)^2 algebra. We then gauge fix kappa-symmetry in the background adapted Killing spinor gauge and present the action in a very simple form.