Dimitrios Tsimpis

Supersymmetric AdS(4) compactifications of IIA supergravity

We derive necessary and sufficient conditions for = 1 compactifications of (massive) IIA supergravity to AdS4 in the language of SU(3) structures. We find new solutions characterized by constant dilaton and nonzero fluxes for all form fields. All fluxes are given in terms of the geometrical data of the internal compact space. The latter is constrained to belong to a special class of half-flat manifolds.

The structure of maximally supersymmetric Yang-Mills theory: constraining higher-order corrections

We solve the superspace Bianchi identities for ten-dimensional supersymmetric Yang-Mills theory without imposing any kind of constraints apart from the standard conventional one. In this way we obtain a set of algebraic conditions on certain fields which in the on-shell theory are constructed as composite ones out of the physical fields. These conditions must hence be satisfied by any kind of theory in ten dimensions invariant under supersymmetry and some, abelian or non-abelian, gauge symmetry. Deformations of the ordinary SYM theory (as well as the fields) are identified as elements of a certain spinorial cohomology, giving control over field redefinitions and the distinction between physically relevant higher-order corrections and those removable by field redefinitions. The conditions derived severely constrain theories involving F2-level terms plus higher-order corrections, as for instance those derived from open strings as effective gauge theories on D-branes.

Script N = 1,2 supersymmetric vacua of IIA supergravity and SU(2) structures

We consider backgrounds of (massive) IIA supergravity of the form of a warped product M1,3 × ωX6, where X6 is a six-dimensional compact manifold and M1,3 is AdS4 or a four-dimensional Minkowski space. We analyse conditions for = 1 and = 2 supersymmetry on manifolds of SU(2) structure. We prove the absence of solutions in certain cases.

AdS4 flux vacua in type II superstrings and their domain-wall solutions

We investigate the emergence of supersymmetric negative-vacuum-energy ground states in four dimensions. First, we rely on the analysis of the effective superpotential, which depends on the background fluxes of the internal manifold, or equivalently has its origin in the underlying gauged supergravity. Four-dimensional, supersymmetric anti-de Sitter vacua with all moduli stabilized appear when appropriate Ramond and Neveu-Schwarz fluxes are introduced in IIA. Geometric fluxes are not necessary. Then the whole setup is analyzed from the perspective of the sources, namely D/NS-branes or Kaluza-Klein monopoles. Orientifold planes are also required for tadpole cancellation. The solutions found in four dimensions correspond to domain walls interpolating between AdS4 and flat spacetime. The various consistency conditions (equations of motion, Bianchi identities and tadpole cancellation conditions) are always satisfied, albeit with source terms. We also speculate on the possibility of assigning (formal) entropies to AdS4 flux vacua via the corresponding dual brane systems.

Fivebrane instantons and Calabi-Yau fourfolds with flux

Using recent results on eleven-dimensional superspace, we compute the contribution of fivebrane instantons with four fermionic zeromodes in M-theory compactifications on Calabi-Yau fourfolds with flux. We find that no superpotential is generated in this case. This result is compatible with a certain flux-dependent modification of the arithmetic genus criterion.

Curved 11D supergeometry

We examine the theta-expansion of the eleven-dimensional supervielbein. We outline a systematic procedure which can be iterated to any order. We give explicit expressions for the vielbein and three-form potential components up to order (θ5). Furthermore we show that at each order in the number of supergravity fields, in a perturbative expansion around flat space, it is possible to obtain exact expressions to all orders in theta. We give the explicit expression at linear order in the number of fields and we show how the procedure can be iterated to any desired order. As a byproduct we obtain the complete linear coupling of the supermembrane to the background supergravity fields, covariantly in component form. We discuss the implications of our results for M(atrix) theory.

Hopf-reductions, fluxes and branes

Abstract We use a series of reductions, T-dualities and liftings to construct connections between fractional brane solutions in IIA, IIB and M-theory. We find a number of phantom branes that are not supported by the geometry, however materialize upon untwisting and/or Hopf-reduction.

Massive IIA supergravities

We perform a systematic search for all possible massive deformations of IIA supergravity in ten dimensions. We show that there exist exactly two possibilities: Romans supergravity and Howe-Lambert-West supergravity. Along the way we give the full details of the ten-dimensional superspace formulation of the latter. The scalar superfield at canonical mass dimension zero (whose lowest component is the dilaton), present in both Romans and massless IIA supergravities, is not introduced from the outset but its existence follows from a certain integrability condition implied by the Bianchi identities. This fact leads to the possibility for a certain topological modification of massless IIA, reflecting an analogous situation in eleven dimensions.

Topological twisting of conformal supercharges

Abstract Putting a twisted version of N = 4 super-Yang–Mills on a curved four-dimensional manifold generically breaks all conformal supersymmetries. In the special case where the four-manifold is a cone, we show that exactly two conformal supercharges remain unbroken. We construct an off-shell formulation of the theory such that the two unbroken conformal supercharges combine into a family of topological charges parameterized by CP 1 . The resulting theory is topological in the sense that it is independent of the metric on the three-dimensional base of the cone.

11D supergravity at Script O(l3)

We compute certain spinorial cohomology groups controlling possible supersymmetric deformations of eleven-dimensional supergravity up to order l3 in the Planck length. At (l) and (l2) the spinorial cohomology groups are trivial and therefore the theory cannot be deformed supersymmetrically. At (l3) the corresponding spinorial cohomology group is generated by a nontrivial element. On an eleven-dimensional manifold M such that p1(M)≠0, this element corresponds to a supersymmetric deformation of the theory, which can only be redefined away at the cost of shifting the quantization condition of the four-form field strength.