Dynamical generation of gauge and Higgs bosons in N=2 supersymmetric non-linear sigma-models (original) (raw)

Nonlinear supersymmetry, brane–bulk interactions and super-Higgs without gravity

Nuclear Physics B, 2010

We derive the coupling of a hypermultiplet of N = 2 global supersymmetry to the Dirac-Born-Infeld Maxwell theory with linear N = 1 and a second nonlinear supersymmetry. At the level of global supersymmetry, this construction corresponds to the interaction with Maxwell brane fields of bulk hypermultiplets, such as the universal dilaton of type IIB strings compactified on a Calabi-Yau manifold. It displays in particular the active role of a four-form field. Constrained N = 1 and N = 2 superfields and the formulation of the hypermultiplet in its single-tensor version are used to derive the nonlinear realization, allowing a fully off-shell description. Exact results with explicit symmetries and supersymmetries are then obtained. The electric-magnetic dual version of the theory is also derived and the gauge structure of the interaction is exemplified with N = 2 nonlinear QED of a charged hypermultiplet. Its Higgs phase describes a novel super-Higgs mechanism without gravity, where the goldstino is combined with half of the hypermultiplet into an N = 1 massive vector multiplet.

Brane dynamics and N = 1 supersymmetric gauge theory

Nuclear Physics B, 1997

We discuss some aspects of the relation between space-time properties of branes in string theory, and the gauge theory on their worldvolume, for models invariant under four supercharges in three and four dimensions. We show that a simple set of rules governing brane dynamics reproduces many features of gauge theory. We study theories with U (N c ), SO(N c ) and Sp(N c ) gauge groups and matter in the fundamental and two index tensor representations, and use the brane description to establish Seiberg's electric-magnetic duality for these models.

N=1 Supersymmetric Standard Models from Intersecting Branes

arXiv (Cornell University), 2004

We construct the first examples of four dimensional three generation N=1 supersymmetric SU(3)cotimesSU(2)LotimesU(1)YSU(3)_c \otimes SU(2)_L \otimes U(1)_YSU(3)cotimesSU(2)LotimesU(1)Y intersecting D6-brane models, that have the spectrum of the N=1 supersymmetric SM and have only a minimal number of (four) massless exotics that constitute a non-chiral set and also have all complex structure moduli naturally fixed by the orbifold symmetry. These models are based on orientifolds of bfT6/(Z3timesZ3){\bf T^6/(Z_3 \times Z_3)}bfT6/(Z3timesZ3) compactifications of IIA theory. The full spectrum of the three generation models accommodates also nuRc\nu_R^cnuRc's and three pairs of MSSM Higgs multiplets. Baryon number is not gauged but as the string scale is geometrically close to the Planck scale proton stability and a solution to the gauge hierarchy problem is guaranteed. A superpotential mu\mumu-term is always present. We also find three stack non-supersymmetric vacua with only the chiral spectrum and gauge group of the SM and no exotics, that possess a N=1 SUSY sector associated with the nuRc\nu_R^cnuRc's which is being used to break the extra U(1) surviving massless the GS mechanism. Also we find five stack non-supersymmetric vacua with exactly the massless chiral spectrum of the N=1 Standard Model + exotic matter, which using tachyonic Higgs excitations flow to only the SM. We point out that in all constructions there is no tree level mass term for the up-quarks.

New Higgs transitions between dual N = 2 string models

Nuclear Physics B, 1997

We describe a new kind of transition between topologically distinct N = 2 type II Calabi-Yau vacua through points with enhanced non-abelian gauge symmetries together with fundamental charged matter hyper multiplets. We connect the appearance of matter to the local geometry of the singularity and discuss the relation between the instanton numbers of the Calabi-Yau manifolds taking part in the transition. In a dual heterotic string theory on K3 × T 2 the process corresponds to Higgsing a semi-classical gauge group or equivalently to a variation of the gauge bundle. In special cases the situation reduces to simple conifold transitions in the Coulomb phase of the non-abelian gauge symmetries.

D-brane models with non-linear supersymmetry

Nuclear Physics B, 2002

We study a class of type I string models with supersymmetry broken on the world-volume of some D-branes and vanishing tree-level potential. Despite the non-supersymmetric spectrum, supersymmetry is non-linearly realized on these D-branes, while it is spontaneously broken in the bulk by Scherk-Schwarz boundary conditions. These models can easily accommodate 3-branes with interesting gauge groups and chiral fermions. We also study the effective field theory and in particular we compute the four-fermion couplings of the localized Goldstino with the matter fermions on the brane. * On leave of absence from CPHT, Ecole Polytechnique, UMR du CNRS 7644. 1 The parameter C f is related to the parametrisation of other authors by C f = − α 4 [17] = C f f 2 [18].

Branes and mirror symmetry in N = 2 supersymmetric gauge theories in three dimensions

Nuclear Physics B, 1997

We use brane configurations and SL(2, Z) symmetry of the type IIB string to construct mirror N = 2 supersymmetric gauge theories in three dimensions. The mirror map exchanges Higgs and Coulomb branches, Fayet-Iliopoulos and mass parameters and U(1) R symmetries. Some quantities that are determined at the quantum level in one theory are determined at the classical level of the mirror. One such example is the complex structure of the Coulomb branch of one theory, which is determined quantum mechanically. It is mapped to the complex structure of the Higgs branch of the mirror theory, which is determined classically. We study the generation of N = 2 superpotentials by open D-string instantons in the brane configurations.

Making manifest the symmetry enhancement for coinciding BPS branes

Lecture Notes in Physics, 1999

We consider g coincident M-5-branes on top of each other, in the KK monopole background Q of multiplicity N . The worldvolume of each M-5-brane is supposed to be given by the local product of the four-dimensional spacetime R 1,3 and an elliptic curve. In the coincidence limit, all these curves yield a single (Seiberg-Witten) hyperelliptic curve Σg, while the gauge symmetry is enhanced to U (N ). We make this gauge symmetry enhancement manifest by considering the hypermultiplet LEEA which is given by the spacetime N=2 non-linear sigma-model (NLSM) having Q as the target space. The hyper-Kähler manifold Q is given by the multicentre Taub-NUT space, which in the coincidence limit amounts to the multiple Eguchi-Hanson (ALE) space QmEH. The NLSM is most naturally described in terms of the hyper-Kähler coset construction on SU (N, N )/U (N ) in harmonic superspace, by using the auxiliary (in classical theory) N=2 vector superfields as Lagrange multipliers, with FI terms resolving the AN singularity. The Maldacena limit, in which the hypermultiplet LEEA becomes extended to the N=4 SYM with the gauge group U (N ), arises in quantum field theory due to a dynamical generation of the N=2 vector and hypermultipet superfields, when sending the FI terms to zero.