Non-geometric orbifolds and wrapping rules

We show that the number of half-supersymmetric p-branes in the Type II theories compactified on orbifolds is determined by the wrapping rules recently introduced, provided that one accounts correctly for both geometric and non-geometric T-dual configurations. Starting from the Type II theories compactified on K3, we analyze their toroidal dimensional reductions, showing how the resulting half-supersymmetric p-branes satisfy the wrapping rules only by taking into account all the possible higher-dimensional origins. We then consider Type II theories compactified on the orbifold T^6/(Z_2 \times Z_2 ), whose massless four-dimensional theory is an N=2 supergravity. Again, the wrapping rules are obeyed only if one includes the complete orbit of the T-duality group, namely either Type IIA or Type IIB theories compactified on either the geometric or the non-geometric T-dual orbifold. Finally, we comment on the interpretation of our results in the framework of the duality between the Heterotic string compactified on K3 \times T^2 and the Type II string compactified on a Calabi-Yau threefold.Comment: 26 pages, 8 table

The Universality of M-branes

We review the evidence for the various dualities amongst the five D=10 superstring theories and for the existence of M-theory using the associated effective supergravity theories. We also summarise the combinatorial technics developed for constructing BPS solutions in D=11 supergravity theory and conjecture that all the BPS solutions of D<11 supergravity theories can be derived from the BPS solutions of D=11 supergravity that preserve 1/2 the supersymmetry. To demonstrate this, we derive the dyonic p-brane solutions from eleven dimensions.Comment: Many changes have been made in the text and some references have been added. 8 pages, Latex, Talk at the Imperial College Workshop 5-10 Jul

Towards a classification of branes in theories with eight supercharges

We provide a classification of half-supersymmetric branes in quarter-maximal supergravity theories with scalars parametrising coset manifolds. Guided by the results previously obtained for the half-maximal theories, we are able to show that half-supersymmetric branes correspond to the real longest weights of the representations of the brane charges, where the reality properties of the weights are determined from the Tits-Satake diagrams associated to the global symmetry groups. We show that the resulting brane structure is universal for all theories that can be uplifted to six dimensions. We also show that when viewing these theories as low-energy theories for the suitably compactified heterotic string, the classification we obtain is in perfect agreement with the wrapping rules derived in previous works for the same theory compactified on tori. Finally, we relate the branes to the R-symmetry representations of the central charges and we show that in general the degeneracies of the BPS conditions are twice those of the half-maximal theories and four times those of the maximal ones.Comment: 47 pages, 8 figure

Swampland Bounds on the Abelian Gauge Sector

We derive bounds on the number of abelian gauge group factors in six-dimensional gravitational theories with minimal supersymmetry and in their F-theoretic realisations. These bounds follow by requiring consistency of certain BPS strings in the spectrum of the theory, as recently proposed in the literature. Under certain assumptions this approach constrains the number of abelian gauge group factors in six-dimensional supergravity theories with at least one tensor multiplet to be $N \leq 20$ (or $N \leq 22$ in absence of charged matter). For any geometric F-theory realisation with at least one tensor multiplet we establish the bound $N \leq 16$ by demanding unitarity of a heterotic solitonic string which exists even in absence of a perturbative heterotic dual. This result extends to four-dimensional F-theory vacua on any blowup of a rational fibration. Our findings lead to universal bounds on the rank of the Mordell-Weil group of elliptically fibered Calabi-Yau threefolds.Comment: 10 pages, 2-column forma

Spacetime Instanton Corrections in 4D String Vacua - The Seesaw Mechanism for D-Brane Models

We systematically investigate instanton corrections from wrapped Euclidean D-branes to the matter field superpotential of various classes of N=1 supersymmetric D-brane models in four dimensions. Both gauge invariance and the counting of fermionic zero modes provide strong constraints on the allowed non-perturbative superpotential couplings. We outline how the complete instanton computation boils down to the computation of open string disc diagrams for boundary changing operators multiplied by a one-loop vacuum diagram. For concreteness we focus on E2-instanton effects in Type IIA vacua with intersecting D6-branes, however the same structure emerges for Type IIB and heterotic vacua. The instantons wrapping rigid cycles can potentially destabilise the vacuum or generate perturbatively absent matter couplings such as proton decay operators, mu-parameter or right-handed neutrino Majorana mass terms. The latter allow the realization of the seesaw mechanism for MSSM-like intersecting D-brane models.Comment: 40 pages, 3 tables, 7 figures; v2: typos corrected, references added; v3: minor sign adjustments, some comments added; v4: published versio

Supersymmetric dyonic black holes of IIA string on Six Torus

A class of four-dimensional static supersymmetric black hole solutions of effective supergravity Lagrangian of IIA superstring compactified on $T^6$ is constructed by explicitly solving Killing spinor equations (KSEs). These solutions are dyonic black holes parametrized by four charges, with dilaton and diagonal internal metric components as the only non-zero scalar fields, and preserve $1 \over 8$ of $N=8$ supersymmetry. The KSEs with only Neveu-Schwarz-Neveu-Schwarz charges relate spinors with opposite chirality from ten-dimensional view point, and have identical structures with KSEs of toroidally compactified heterotic string. We also find a solution with four Ramond-Ramond charges which is U-dual to the solution with four Neveu-Schwarz-Neveu-Schwarz charges, and corresponds to the intersecting D-brane configuration with two 2-branes and two 4-branes. A configuration with both Neveu-Schwarz-Neveu-Schwarz charges and Ramond-Ramond charges is also found. We show that the configurations T-dual to the above solutions are also solutions of the KSEs. The patterns of supersymmetry breaking are studied in detail.Comment: LaTeX with RevTeX, 41 page

Lectures on Superstring and M Theory Dualities

These lectures begin by reviewing the evidence for S duality of the toroidally compactified heterotic string in 4d that was obtained in the period 1992--94. Next they review recently discovered dualities that relate all five of the 10d superstring theories and a quantum extension of 11d supergravity called M theory. The study of p-branes of various dimensions (some of which are D-branes) plays a central role. The final sections survey supersymmetric string vacua in 6d and some of the dual constructions by which they can be obtained. Special emphasis is given to a class of N=1 models that exhibit ``heterotic-heterotic duality.''Comment: 67 pages, latex, 1 figure; Lectures given at the ICTP Spring School (March 1996) and the TASI Summer School (June 1996), TASI9

Open string instantons and superpotentials

We study the F-terms in N=1 supersymmetric, d=4 gauge theories arising from D(p+3)-branes wrapping supersymmetric p-cycles in a Calabi-Yau threefold. If p is even the spectrum and superpotential for a single brane are determined by purely classical ($\alpha^\prime \to 0$) considerations. If p=3, superpotentials for massless modes are forbidden to all orders in $\alpha^\prime$ and may only be generated by open string instantons. For this latter case we find that such instanton effects are generically present. Mirror symmetry relates even and odd p and thus perturbative and nonperturbative superpotentials; we provide a preliminary discussion of a class of examples of such mirror pairs.Comment: 22 pages, harvmac big; v2, corrected some typo