Herve Partouche

Spontaneous breaking of N = 2 global supersymmetry

Abstract We study spontaneous supersymmetry breaking in N = 2 globally supersymmetric theories describing a system of abelian vector multiplets. We find that the most general form of the action admits, in addition to the usual Fayet-Iliopoulos term, a magnetic Fayet-Iliopoulos term for the auxiliary components of dual vector multiplets. In a generic case, N = 2 supersymmetry is broken down spontaneously to N = 1. In some cases however, the scalar potential can drive the theory towards a N = 2 supersymmetric ground state where massless dyons condense in the vacuum.

Aspects of type I– type II– heterotic triality in four dimensions

We discuss the equivalence between Type I, Type II and Heterotic N = 2 superstring theories in four dimensions. We study the effective field theory of Type I models obtained by orientifold reductions of Type IIB compactifications on K3 × T 2 . We show that the perturbative prepotential is determined by the one-loop corrections to the Planck mass and is associated to an index. As is the case for threshold corrections to gauge couplings, this renormalization is entirely due to N = 2 BPS states that originate from D = 6 massless string modes. We apply our result to the so-called S-T-U model which admits simultaneous Type II and Heterotic descriptions, and show that all three prepotentials agree in the appropriate limits as expected from the superstring triality conjecture.

Rolling among G2 vacua

We consider topology-changing transitions between 7-manifolds of holonomy G2 constructed as a quotient of CY ? S1 by an antiholomorphic involution. We classify involutions for Complete Intersection CY threefolds, focussing primarily on cases without fixed points. The ordinary conifold transition between CY threefolds descends to a transition between G2 manifolds, corresponding in the = 1 effective theory incorporating the light black hole states either to a change of branch in the scalar potential or to a Higgs mechanism. A simple example of conifold transition with a fixed nodal point is also discussed. As a spin-off, we obtain examples of G2 manifolds with the same value for the sum of Betti numbers b2+b3, and hence potential candidates for mirror manifolds.

Phases of supersymmetric gauge theories from M-theory on G2 manifolds

We consider M-theory on compact spaces of G2 holonomy constructed as orbifolds of the form (CY × S1)/2 with fixed point set Σ on the CY. This describes = 1 SU(2) gauge theories with b1(Σ) chiral multiplets in the adjoint. For b1 = 0, it generalizes to compact manifolds the study of the phase transition from the non-abelian to the confining phase through geometrical S3 flops. For b1 = 1, the non-abelian and Coulomb phases are realized, where the latter arises by desingularization of the fixed point set, while an S2 × S1 flop occurs. In addition, an extremal transition between G2 spaces can take place at conifold points of the CY moduli space where unoriented membranes wrapped on 1 and 2 become massless.

Induced superstring cosmologies and moduli stabilization

Abstract We extend the analysis of the recently obtained stringy cosmological solutions induced by thermal and quantum effects, once space–time supersymmetry is spontaneously broken by geometrical fluxes. Cases in which more than one modulus participating in the supersymmetry breaking mechanism are investigated. The free energy is obtained at the full string level. In the intermediate cosmological region where the temperature and the supersymmetry breaking scale are sufficiently smaller than the Hagedorn temperature, the quantum and thermal corrections are under control and calculable. The reason is that the contributions to the effective potential of the moduli that are not participating in the supersymmetry breaking are exponentially suppressed. The backreaction on the initially flat background results in many cases into cosmological evolutions, where the dynamics of all complex structure moduli is frozen. The solutions describe effectively a radiation dominated era, where thermal effects are never negligible, even if the temperature tends to zero at late times. We analyze several types of supersymmetry breaking patterns and examine the stability of the corresponding radiation era.

Exact monodromy group of N = 2 heterotic superstring

Abstract We describe an N = 2 heterotic superstring model of rank 3 which is dual to the type II string compactified on a Calabi-Yau manifold with Betti numbers b 1,1 = 2 and b 1,2 = 86. We show that the exact duality symmetry found from the type II realization contains the perturbative duality group of the heterotic model, as well as the exact quantum monodromies of the rigid SU (2) super-Yang-Mills theory. Moreover, it contains a non-perturbative monodromy which is stringy in origin and corresponds roughly to an exchange of the string coupling with the compactification radius.

Partial spontaneous breaking of global supersymmetry

Abstract We review in detail the recently discovered phenomenon of partial spontaneous breaking of supersymmetry in the case of a N = 2 pure gauge U(1) theory, and recall how the standard lore no go theorem is evaded. We discuss the extension of this mechanism to theories with charged matter, and surprisingly find that the gauging forbids the existence of a magnetic Fayet-Iliopoulos term.

Duality of N = 2 heterotic-type I compactifications in four dimensions

We discuss type I-heterotic duality in four-dimensional models obtained as a Coulomb phase of the six-dimensional U(16) orientifold model compactified on T2 with arbitrary SU(16) Wilson lines. We show that Kahler potentials, gauge threshold corrections and the infinite tower of higher derivative F-terms agree in the limit that corresponds to weak coupling, large T2 heterotic compactifications. On the type I side, all these quantities are completely determined by the spectrum of N = 2 BPS states that originate from D = 6 massless superstring modes.

Non-singular string cosmology in a 2d hybrid model

Abstract The existence of non-singular string cosmologies is established in a class of two-dimensional supersymmetric Hybrid models at finite temperature. The left-moving sector of the Hybrid models gives rise to 16 real ( N 4 = 4 ) spacetime supercharges as in the usual superstring models. The right-moving sector is non-supersymmetric at the massless level, but is characterized by MSDS symmetry, which ensures boson/fermion degeneracy of the right-moving massive levels. Finite temperature configurations, which are free of Hagedorn instabilities, are constructed in the presence of non-trivial “gravito-magnetic” fluxes. These fluxes inject non-trivial winding charge into the thermal vacuum and restore the thermal T-duality symmetry associated with the Euclidean time circle. Thanks to the unbroken right-moving MSDS symmetry, the one-loop string partition function is exactly calculable beyond any α ′ -approximation. At the self-dual point new massless thermal states appear, sourcing localized spacelike branes, which can be used to connect a contracting thermal Universe to an expanding one. The resulting bouncing cosmology is free of any curvature singularities and the string coupling remains perturbative throughout the cosmological evolution.

Cosmological phases of the string thermal effective potential

In a superstring framework, the free energy density F can be determined unambiguously at the full string level once supersymmetry is spontaneously broken via geometrical fluxes. We show explicitly that only the moduli associated to the supersymmetry breaking may give relevant contributions. All other spectator moduli μI give exponentially suppressed contributions for relatively small (as compared to the string scale) temperature T and supersymmetry breaking scale M. More concisely, for μI>T and M, F takes the form F(T,M;μI)=F(T,M)+O[exp(−μIT),exp(−μIM)]. We study the cosmological regime where T and M are below the Hagedorn temperature scale TH. In this regime, F remains finite for any values of the spectator moduli μI. We investigate extensively the case of one spectator modulus μd corresponding to Rd, the radius-modulus field of an internal compactified dimension. We show that its thermal effective potential V(T,M;μ)=F(T,M;μ) admits five phases, each of which can be described by a distinct but different effective field theory. For late cosmological times, the Universe is attracted to a “Radiation-like evolution” with M(t)∝T(t)∝1/a(t)∝t−2/d. The spectator modulus μ(t) is stabilized either to the stringy enhanced symmetry point where Rd=1, or fixed at an arbitrary constant μ0>T,M. For arbitrary boundary conditions at some initial time, tE, μ(t) may pass through more than one effective field theory phase before its final attraction.