A heterotic sigma model with novel target geometry

We construct a (1,2) heterotic sigma model whose target space geometry consists of a transitive Lie algebroid with complex structure on a Kaehler manifold. We show that, under certain geometrical and topological conditions, there are two distinguished topological half--twists of the heterotic sigma model leading to A and B type half--topological models. Each of these models is characterized by the usual topological BRST operator, stemming from the heterotic (0,2) supersymmetry, and a second BRST operator anticommuting with the former, originating from the (1,0) supersymmetry. These BRST operators combined in a certain way provide each half--topological model with two inequivalent BRST structures and, correspondingly, two distinct perturbative chiral algebras and chiral rings. The latter are studied in detail and characterized geometrically in terms of Lie algebroid cohomology in the quasiclassical limit.Comment: 83 pages, no figures, 2 references adde

2d Gauge Theories and Generalized Geometry

We show that in the context of two-dimensional sigma models minimal coupling of an ordinary rigid symmetry Lie algebra $\mathfrak{g}$ leads naturally to the appearance of the "generalized tangent bundle" $\mathbb{T}M \equiv TM \oplus T^*M$ by means of composite fields. Gauge transformations of the composite fields follow the Courant bracket, closing upon the choice of a Dirac structure $D \subset \mathbb{T}M$ (or, more generally, the choide of a "small Dirac-Rinehart sheaf" $\cal{D}$), in which the fields as well as the symmetry parameters are to take values. In these new variables, the gauge theory takes the form of a (non-topological) Dirac sigma model, which is applicable in a more general context and proves to be universal in two space-time dimensions: A gauging of $\mathfrak{g}$ of a standard sigma model with Wess-Zumino term exists, \emph{iff} there is a prolongation of the rigid symmetry to a Lie algebroid morphism from the action Lie algebroid $M \times \mathfrak{g}\to M$ into $D\to M$ (or the algebraic analogue of the morphism in the case of $\cal{D}$). The gauged sigma model results from a pullback by this morphism from the Dirac sigma model, which proves to be universal in two-spacetime dimensions in this sense.Comment: 22 pages, 2 figures; To appear in Journal of High Energy Physic

The group structure of non-Abelian NS-NS transformations

We study the transformations of the worldvolume fields of a system of multiple coinciding D-branes under gauge transformations of the supergravity Kalb-Ramond field. We find that the pure gauge part of these NS-NS transformations can be written as a U(N) symmetry of the underlying Yang-Mills group, but that in general the full NS-NS variations get mixed up non-trivially with the U(N). We compute the commutation relations and the Jacobi identities of the bigger group formed by the NS-NS and U(N) transformations.Comment: Latex, 11 pages. v2: Typos corrected; version to appear in JHEP

Generalized Geometry and M theory

We reformulate the Hamiltonian form of bosonic eleven dimensional supergravity in terms of an object that unifies the three-form and the metric. For the case of four spatial dimensions, the duality group is manifest and the metric and C-field are on an equal footing even though no dimensional reduction is required for our results to hold. One may also describe our results using the generalized geometry that emerges from membrane duality. The relationship between the twisted Courant algebra and the gauge symmetries of eleven dimensional supergravity are described in detail.Comment: 29 pages of Latex, v2 References added, typos fixed, v3 corrected kinetic term and references adde

Heterotic Sigma Models with N=2 Space-Time Supersymmetry

We study the non-linear sigma model realization of a heterotic vacuum with N=2 space-time supersymmetry. We examine the requirements of (0,2) + (0,4) world-sheet supersymmetry and show that a geometric vacuum must be described by a principal two-torus bundle over a K3 manifold.Comment: 20 pages, uses xy-pic; v3: typos corrected, reference added, discussion of constraints on Hermitian form modifie

No Forbidden Landscape in String/M-theory

Scale invariant but non-conformal field theories are forbidden in (1+1) dimension, and so should be the corresponding holographic dual gravity theories. We conjecture that such scale invariant but non-conformal field configurations do not exist in the string/M-theory. We provide a proof of this conjecture in the classical supergravity limit under a certain gauge condition. Our proof does also apply in higher dimensional scale invariant but non-conformal field configurations, which suggests that scale invariant but non-conformal field theories may be forbidden in higher dimensions as well.Comment: 14 pages, v2: energy condition on c-theorem is corrected, v3: extra assumption in the proof is discussed due to a sign error in the previous versio

T-duality and closed string non-commutative (doubled) geometry

We provide some evidence that closed string coordinates will become non-commutative turning on H-field flux background in closed string compactifications. This is in analogy to open string non-commutativity on the world volume of D-branes with B- and F-field background. The class of 3-dimensional backgrounds we are studying are twisted tori (fibrations of a 2-torus over a circle) and the their T-dual H-field, 3-form flux backgrounds (T-folds). The spatial non-commutativity arises due to the non-trivial monodromies of the toroidal Kahler resp. complex structure moduli fields, when going around the closed string along the circle direction. In addition we study closed string non-commutativity in the context of doubled geometry, where we argue that in general a non-commutative closed string background is T-dual to a commutative closed string background and vice versa. Finally, in analogy to open string boundary conditions, we also argue that closed string momentum and winding modes define in some sense D-branes in closed string doubled geometry.Comment: 31 pages, references added, extended version contains new sections 3.3., 3.4 and

Super-Yang-Mills and M5-branes

We uplift 5-dimensional super-Yang-Mills theory to a 6-dimensional gauge theory with the help of a space-like constant vector $\eta^M$, whose norm determines the Yang-Mills coupling constant. After the localization of $\eta^M$ the 6D gauge theory acquires Lorentzian invariance as well as scale invariance. We discuss KK states, instantons and the flux quantization. The 6D theory admits extended solutions like 1/2 BPS `strings' and monopoles.Comment: 15 pages; minor changes, to appear in JHE

Heterotic-Type II duality in the hypermultiplet sector

We revisit the duality between heterotic string theory compactified on K3 x T^2 and type IIA compactified on a Calabi-Yau threefold X in the hypermultiplet sector. We derive an explicit map between the field variables of the respective moduli spaces at the level of the classical effective actions. We determine the parametrization of the K3 moduli space consistent with the Ferrara-Sabharwal form. From the expression of the holomorphic prepotential we are led to conjecture that both X and its mirror must be K3 fibrations in order for the type IIA theory to have an heterotic dual. We then focus on the region of the moduli space where the metric is expressed in terms of a prepotential on both sides of the duality. Applying the duality we derive the heterotic hypermultiplet metric for a gauge bundle which is reduced to 24 point-like instantons. This result is confirmed by using the duality between the heterotic theory on T^3 and M-theory on K3. We finally study the hyper-Kaehler metric on the moduli space of an SU(2) bundle on K3.Comment: 27 pages; references added, typos correcte

Novel Branches of (0,2) Theories

We show that recently proposed linear sigma models with torsion can be obtained from unconventional branches of conventional gauge theories. This observation puts models with log interactions on firm footing. If non-anomalous multiplets are integrated out, the resulting low-energy theory involves log interactions of neutral fields. For these cases, we find a sigma model geometry which is both non-toric and includes brane sources. These are heterotic sigma models with branes. Surprisingly, there are massive models with compact complex non-Kahler target spaces, which include brane/anti-brane sources. The simplest conformal models describe wrapped heterotic NS5-branes. We present examples of both types.Comment: 36 pages, LaTeX, 2 figures; typo in Appendix fixed; references added and additional minor change