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We construct integrable deformations of the λ-type for asymmetrically gauged WZW models. This is achieved by a modification of the Sfetsos gauging procedure to account for a possible automorphism that is allowed in G/G models. We verify classical integrability, derive the one-loop beta function for the deformation parameter and give the construction of integrable D-brane configurations in these models. As an application, we detail the case of the λ-deformation of the cigar geometry corresponding to the axial gauged SL(2, R)/U(1) theory at large k. Here we also exhibit a range of both A-type and B-type integrability preserving D-brane configurations.

We investigate the integrable Yang-Baxter deformation of the 2d Principal Chiral Model with a Wess-Zumino term. For arbitrary groups, the one-loop beta functions are calculated and display a surprising connection between classical and quantum physics: the classical integrability condition is necessary to prevent new couplings being generated by renormalisation. We show these theories admit an elegant realisation of Poisson-Lie T-duality acting as a simple inversion of coupling constants. The self-dual point corresponds to the Wess-Zumino-Witten model and is the IR fixed point under RG. We address the possibility of having supersymmetric extensions of these models showing that extended supersymmetry is not possible in general., Comment: 44 pages; 4 figures; v2: references added; v3: published version, text edited and restructured, result added on CFT operators driving the flow

We clarify the relation between various approaches to the manifestly T-duality symmetric string. We explain in detail how the PST covariant doubled string arises from an unusual gauge fixing. We pay careful attention to the role of "spectator" fields in this process and also show how the T-duality invariant doubled dilaton emerges naturally. We extend these ideas to non-Abelian T-duality and show they give rise to the duality invariant formalism based on the semi-Abelian Drinfeld Double. We then develop the N=(0,1) supersymmetric duality invariant formalism., Comment: 29 pages; v2: references corrected in introduction; v3: matches journal version, references added, very minor changes to text

We present an N = 2 world-sheet superspace description of D-branes on bihermitian or generalized Kaehler manifolds. To accomplish this, D-branes are considered as boundary conditions for a nonlinear sigma-model in what we call N = 2 boundary superspace. In this note the general formalism for such an approach is presented and the resulting classification sketched. This includes some remarks regarding target spaces whose parameterization includes semi-chiral superfields which have not appeared in the literature yet. In an accompanying note we turn to some examples and applications of the general setup presented here.

Motivated by the results in hep-th/0508228 , we perform a careful analysis of the allowed linear constraints on N = ( 2 , 2 ) scalar superfields. We show that only chiral, twisted-chiral and semi-chiral superfields are possible. Various subtleties are discussed.

Motivated by a system consisting of a number of parallel M5-branes, we study possible local deformations of a chiral two-form in six dimensions. Working to first order in the coupling constant, this reduces to the study of the local BRST cohomological group at ghost number zero. We obtain an exhaustive list of all possible deformations. None of them allows for a satisfactory formulation of the M5-branes system leading to the conclusion that no local field theory can describe such a system., 7 pages, LaTeX, minor corrections, assumptions more clearly stated, final version which will appear in Phys. Lett. B

We study d=2, N=(2,2) non-linear sigma-models in (2,2) superspace. By analyzing the most general constraints on a superfield, we show that through an appropriate choice of coordinates, there are no other superfields than chiral, twisted chiral and semi-chiral ones. We study the resulting sigma-models and we speculate on the possibility that all (2,2) non-linear sigma-models can be described using these fields. We apply the results to two examples: the SU(2) x U(1) and the SU(2) x SU(2) WZW model. Pending upon the choice of complex structures, the former can be described in terms of either one semi-chiral multiplet or a chiral and a twisted chiral multiplet. The latter is formulated in terms of one semi-chiral and one twisted chiral multiplet. For both cases we obtain the potential explicitely., 22 pages, LaTeX

In this note we extend the Pasti-Sorokin-Tonin formalism for chiral bosons in two dimensions to $N=(1,1)$ and $N=(2,2)$ superspace. In the latter case the formalism is developed for chiral, twisted chiral and semi-chiral superfields., Comment: 22 pages

We review N=(2,2) supersymmetric non-linear sigma-models in two dimensions and their relation to generalized Kahler and Calabi-Yau geometry. We illustrate this with an explicit non-trivial example., Comment: 19 pages. Proceedings of the Corfu Summer Institute 2012, September 8-27, 2012

N=(2,2), d=2 supersymmetric non-linear sigma-models provide a physical realization of Hitchin's and Gualtieri's generalized Kaehler geometry. A large subclass of such models are comprised by WZW-models on even-dimensional reductive group manifolds. In the present paper we analyze the complex structures, type changing, the superfield content and the affine isometries compatible with the extra supersymmetry. The results are illustrated by an exhaustive discussion of the N=(2,2) WZW-models on S3xS1 and S3xS3 where various aspects of generalized Kaehler and Calabi-Yau geometry are verified and clarified. The examples illustrate a slightly weaker definition for an N=(2,2) superconformal generalized Kaehler geometry compared to that for a generalized Calabi-Yau geometry., LaTeX, 51 pages, Typo's corrected, discussion on superconformal vs. generalized Calabi-Yau fine tuned

As a preparation for the study of {\it arbitrary} extensions of $d=2$ gravity we present a detailed investigation of $SO(N)$ supergravity. By gauging a chiral, nilpotent subgroup of the $OSp(N|2)$ Wess-Zumino-Witten model we obtain an all order expression for the effective action. Reality of the coupling constant imposes the usual restrictions on $c$ for $N=0$ and 1. No such restrictions appear for $N\geq 2$. For $N=2$, 3 and 4, no renormalizations of the coupling constant beyond one loop occur. These results are related to non-renormalization theorems for theories with extended supersymmetries. Arbitrary (super)extensions of $d=2$ gravity are then analyzed. The induced theory is represented by a WZW model for which a chiral, solvable group is gauged. From this, we obtain the effective action. All order expressions for both the coupling constant renormalization and the wavefunction renormalization are given. From this we classify all extensions of $d=2$ gravity for which the coupling constant gets at most a one loop renormalization. As an application of the general strategy, $N=4$ theories based on $D(2,1,\a)$ and $SU(1,1|2)$, all $WA$ gravities and the $N=2$ $W_n$ models are treated in some detail., Comment: 58 pages, latex, LBL-33738, UCB-PTH-93/06, KUL-TF-93/09

Following the general formalism reviewed in 0810.5355 [hep-th] we present several examples of possible D3-brane configurations on four-dimensional generalized Kaehler geometries. We will discuss T-duality transformations in N = 2 boundary superspace and apply the duality transformations to the constructed D3-branes. The duality transformations lead to a systematic method to construct coisotropic branes, even on target spaces that are not hyper-Kaehler., 7 pages, contribution to the proceedings of the Fourth Workshop of the RTN project 'Constituents, Fundamental Forces and Symmetries of the Universe', Varna, September 11 - 17, 2008; some typos corrected

We complete the investigation of N=(2,2) supersymmetric nonlinear sigma-models in the presence of a boundary. We study the full bihermitian geometry parameterized by chiral, twisted chiral and semi-chiral superfields and identify the D-brane configurations preserving an N=2 worldsheet supersymmetry. Combining twisted with semi-chiral superfields leads to a clearly defined notion of lagrangian and coisotropic branes generalizing lagrangian and coisotropic A-branes on Kahler manifolds to manifolds which are not necessarily Kahler (but still bihermitian). Adding chiral fields complicates the picture and results in hybrid configurations interpolating between lagrangian/coisotropic branes and branes wrapping around a holomorphic cycle. Even here the branes can be viewed as coisotropic submanifolds albeit in a generalized sense. All supersymmetric D-brane configurations are characterized in the context of generalized complex geometry. Duality transformations interchanging the various types of superfields while preserving all supersymmetries are explicitly constructed and provide for a powerful technique to construct various highly non-trivial D-brane configurations. Several explicit examples are given., LaTeX, JHEP3.cls, 57 pages

We present the beginnings of a new consistent gauge theory with spin 2 and spin 3 gauge fields in two dimensions. It is based on a nonlinear Lie algebra, whose “gauging” is discussed in detail. (The present treatment of the gauge sector is expanded as compared to [3]). For the coupling to matter, we introduce the concept of a “nested covariant derivative”, and we obtain an invariant action by solving a functional integrability condition. It reads

We present a manifestly supersymmetric description of A and B branes on Kaehler manifolds using a completely local N=2 superspace formulation of the world-sheet nonlinear sigma-model in the presence of a boundary. In particular, we show that an N=2 superspace description of type A boundaries is possible. This leads to a concrete realization of the still poorly understood coisotropic A branes. We also discuss briefly how the superspace description of a B brane provides an efficient way to compute higher loop beta-functions. In particular, we sketch how one obtains the fourth order derivative correction to the Born-Infeld action by using a beta-function method., 8 pages, contribution to the proceedings of the Third Workshop of the RTN project 'Constituents, Fundamental Forces and Symmetries of the Universe', Valencia, October 1 - 5, 2007

We give a manifest supersymmetric description of A and B branes on Kahler manifolds using a completely local N=2 superspace formulation of the world-sheet nonlinear sigma-model in the presence of a boundary. In particular, we show that an N=2 superspace description of type A boundaries is possible, at least when the background is Kahler. This leads to an elegant and concrete setting for studying coisotropic A branes. Here, apgesan important role is played by the boundary potential, whose precise physical meaning remains to be fully understood. Duality transformations relating A and B branes in the presence of isometries are studied as well., Comment: LaTeX, 32 pages

Motivated by the results in {\tt hep-th/0508228}, we perform a careful analysis of the allowed linear constraints on $N=(2,2)$ scalar superfields. We show that only chiral, twisted-chiral and semi-chiral superfields are possible. Various subtleties are discussed., 11 pages, LaTeX2e

A brief, non-technical and non-exhaustive review of D(irichlet)-branes and (some) of their applications is given., Comment: 10 pages, 5 figures, contribution to the proceedings of XXXIXth Rencontres de Moriond on Electroweak Interactions and Unified Theories, references added

We introduce and review several indirect methods to calculate the effective action for a single D-brane or a set of coinciding D-branes., 7 pages, LaTeX, needs fortschritte.sty, contribution to the proccedings of the 37th International Symposium Ahrenshoop

Recently a proposal for the non-abelian effective D-brane action was given through fourth order in alpha'. As the resulting expressions turned out to be quite involved, some checks of this result are called for. In the present paper we calculate the spectrum in the presence of constant magnetic background fields and compare it to the string theoretical result. Apart from a small typo in the original expression (the overall sign of thefourth order term), we obtain perfect agreement. We discuss potential applications., 13 pages, LaTeX2e

We study two-dimensional supersymmetric non-linear sigma-models with boundaries. We derive the most general family of boundary conditions in the non-supersymmetric case. Next we show that no further conditions arise when passing to the N=1 model. We present a manifest N=1 off-shell formulation. The analysis is greatly simplified compared to previous studies and there is no need to introduce non-local superspaces nor to go (partially) on-shell. Whether or not torsion is present does not modify the discussion. Subsequently, we determine under which conditions a second supersymmetry exists. As for the case without boundaries, two covariantly constant complex structures are needed. However, because of the presence of the boundary, one gets expressed in terms of the other one and the remainder of the geometric data. Finally we recast some of our results in N=2 superspace and discuss applications., LaTeX, 23 pages

We review a method to find the non-abelian open superstring effective action, thereby settling the issue of the ordering ambiguities. We start from solutions to Yang-Mills which, in D-brane context, define certain BPS configurations. Studying their deformations in the abelian case shows that the Born-Infeld action is the unique deformation which admits solutions of this type. By applying the method to the non-abelian case we calculated the full effective action through O(\alpha'^3). The presence of derivative terms turns out to be essential. Testing the result by comparing the spectrum in the presence of a constant magnetic background field with the string theory prediction, we obtain perfect agreement., Comment: 6 pages, proceedings of the Corfu 2001 RTN meeting

Recently the construction of the non-abelian effective D-brane action was performed through order $\alpha'{}^3$ including the terms quadratic in the gauginos. This result can be tested by calculating the spectrum in the presence of constant magnetic background fields and comparing it to the string theoretic predictions. This test was already performed for the purely bosonic terms. In this note we extend the test to the fermionic terms. We obtain perfect agreement., Comment: 10 pages, LaTeX

Using the method developed in {\tt hep-th/0103015}, we determine the non-abelian Born-Infeld action through ${\cal O}(\alpha'{}^3)$. We start from solutions to a Yang-Mills theory which define a stable holomorphic vector bundle. Subsequently we investigate its deformation away from this limit. Through $ {\cal O}(\alpha'{}^2)$, a unique, modulo field redefinitions, solution emerges. At $ {\cal O}(\alpha'{}^3)$ we find a one-parameter family of allowed deformations. The presence of derivative terms turns out to be essential. Finally, we present a detailed comparison of our results to existing, partial results., Comment: LaTeX, 29 pages; references added, typos corrected, following suggestions of referee: title, introduction and conclusions altered

Starting from BPS solutions to Yang-Mills which define a stable holomorphic vector bundle, we investigate its deformations. Assuming slowly varying fieldstrengths, we find in the abelian case a unique deformation given by the abelian Born-Infeld action. We obtain the deformed Donaldson-Uhlenbeck-Yau stability condition to all orders in alpha'. This result provides strong evidence supporting the claim that the only supersymmetric deformation of the abelian d=10 supersymmetric Yang-Mills action is the Born-Infeld action., Comment: 18 pages, 1 figure, LaTeX

To gain insight into the non-abelian Born-Infeld (NBI) action, we study coinciding D-branes wrapped on tori, and turn on magnetic fields on their worldvolume. We then compare predictions for the spectrum of open strings stretching between these D-branes, from perturbative string theory and from the effective NBI action. Under some plausible assumptions, we find corrections to the Str-prescription for the NBI action at order F^6. In the process we give a way to classify terms in the NBI action that can be written in terms of field strengths only, in terms of permutation group theory., Comment: LaTeX, 31 pages, 30 figures

We review an iterative construction of the supersymmetric non-abelian Born-Infeld action. We obtain the action through second order in the fieldstrength. Kappa-invariance fixes the ordenings which turn out to deviate from the symmetrized trace proposal., LaTeX, 8 pages, contribution to the proceedings of the workshop "The Quantum Structure of Spacetime and the Geometric Nature of Fundamental Interactions", Berlin, October 2000

Motivated by the results of Hashimoto and Taylor, we perform a detailed study of the mass spectrum of the non-abelian Born-Infeld theory, defined by the symmetrized trace prescription, on tori with constant magnetic fields turned on. Subsequently, we compare this for several cases to the mass spectrum of intersecting D-branes. Exact agreement is found in only two cases: BPS configurations on the four-torus and coinciding tilted branes. Finally we investigate the fluctuation dynamics of an arbitrarily wrapped Dp-brane with flux., Comment: LaTeX, 23 pages, 1 figure included