An ansatz for a non-perturbative four-graviton amplitude in type IIB superstring theory

A natural SL(2,Z) invariant generalization of the Veneziano amplitude in type IIB superstring theory is investigated. It includes certain perturbative and non-perturbative (D-instanton) contributions, and it reduces to the correct expressions in different limits. The singularities are poles in the $s$-$t$-$u$ channels, corresponding to the exchange of particles with a mass spectrum coinciding with that of $(p,q)$ string states. We describe the general structure of the associated perturbative corrections to the effective action.Comment: Version appeared in Phys.Lett. B. Discussion expanded. 7 pages, harvma

Hyperbolic Spaces in String and M-Theory

We describe string-theory and $d=11$ supergravity solutions involving symmetric spaces of constant negative curvature. Many examples of non-supersymmetric string compactifications on hyperbolic spaces $H_r$ of finite volume are given in terms of suitable cosets of the form $H_r/\Gamma$, where $\Gamma$ is a discrete group. We describe in some detail the cases of the non-compact hyperbolic spaces $F_2$ and $F_3$, representing the fundamental regions of $H_2$ and $H_3$ under $SL(2,Z)$ and the Picard group, respectively. By writing $AdS$ as a U(1) fibration, we obtain new solutions where $AdS_{2p+1}$ gets untwisted by T-duality to ${\bf R}\times SU(p,1)/(SU(p)\times U(1))$. Solutions with time-dependent dilaton field are also constructed by starting with a solution with NS5-brane flux over $H_3$. A new class of non-supersymmetric conformal field theories can be defined via holography.Comment: 17 pages, Latex. Small additions and correction

Supersymmetric fluxbrane intersections and closed string tachyons

We consider NS-NS superstring model with several ``magnetic'' parameters $b_s$ (s=1, ...,N) associated with twists mixing a compact $S^1$ direction with angles in $N$ spatial 2-planes of flat 10-dimensional space. It generalizes the Kaluza-Klein Melvin model which has single parameter $b$. The corresponding U-dual background is a R-R type IIA solution describing an orthogonal intersection of $N$ flux 7-branes. Like the Melvin model, the NS-NS string model with $N$ continuous parameters is explicitly solvable; we present its perturbative spectrum and torus partition function explicitly for the N=2 case. For generic $b_s$ (above some critical values) there are tachyons in the $S^1$ winding sector. A remarkable feature of this model is that while in the Melvin N=1 case all supersymmetry is broken, a fraction of it may be preserved for $N >1$ by making a special choice of the parameters $b_s$. Such solvable NS-NS models may be viewed as continuous-parameter analogs of non-compact orbifold models. They and their U-dual R-R fluxbrane counterparts may have some ``phenomenological'' applications. In particular, in N=3 case one finds a special 1/4 supersymmetric R-R 3-brane background. Putting Dp-branes in flat twisted NS-NS backgrounds leads to world-volume gauge theories with reduced amount of supersymmetry. We also discuss possible ways of evolution of unstable backgrounds towards stable ones.Comment: 26 pages, harvmac. v3: reference added, minor changes in appendi

Exactly solvable string models of curved space-time backgrounds

We consider a new 3-parameter class of exact 4-dimensional solutions in closed string theory and solve the corresponding string model, determining the physical spectrum and the partition function. The background fields (4-metric, antisymmetric tensor, two Kaluza-Klein vector fields, dilaton and modulus) generically describe axially symmetric stationary rotating (electro)magnetic flux-tube type universes. Backgrounds of this class include both the dilatonic (a=1) and Kaluza-Klein (a=\sqrt 3) Melvin solutions and the uniform magnetic field solution, as well as some singular space-times. Solvability of the string sigma model is related to its connection via duality to a simpler model which is a ``twisted" product of a flat 2-space and a space dual to 2-plane. We discuss some physical properties of this model (tachyonic instabilities in the spectrum, gyromagnetic ratios, issue of singularities, etc.). It provides one of the first examples of a consistent solvable conformal string model with explicit D=4 curved space-time interpretation.Comment: 54 pages, harvmac (corrected and extended version

N=2 Chern-Simons-Matter Theories Without Vortices

We study ${\cal N}=2$ Chern-Simons-matter theories with gauge group $U_{k_1}(1)\times U_{k_2}(1)$. We find that, when $k_1+k_2=0$, the partition function computed by localization dramatically simplifies and collapses to a single term. We show that the same condition prevents the theory from having supersymmetric vortex configurations. The theories include mass-deformed ABJM theory with $U(1)_{k}\times U_{-k}(1)$ gauge group as a particular case. Similar features are shared by a class of CS-matter theories with gauge group $U_{k_1}(1)\times \cdots \times U_{k_N}(1)$.Comment: 17 page

Heterotic strings in a uniform magnetic field

An exact conformal model representing a constant magnetic field background in heterotic string theory is explicitly solved in terms of free creation/annihilation operators. The spectrum of physical states is examined for different possible embeddings of the magnetic U(1) subgroup. We find that an arbitrarily small magnetic field gives rise to an infinite number of tachyonic excitations corresponding to charged vector states of the massless level and to higher level states with large spins and charges.Comment: 25 pages, harvmac (few comments added, misprints corrected