The Gross-Neveu Model from String Theory

We study an intersecting D-brane model which at low energies describes (1+1)-dimensional chiral fermions localized at defects on a stack of N_c D4-branes. Fermions at different defects interact via exchange of massless (4+1)-dimensional fields. At weak coupling this interaction gives rise to the Gross-Neveu (GN) model and can be studied using field theoretic techniques. At strong coupling one can describe the system in terms of probe branes propagating in a curved background in string theory. The chiral symmetry is dynamically broken at zero temperature and is restored above a critical temperature T_c which depends on the coupling. The phase transition at T_c is first order at strong coupling and second order at weak coupling.Comment: 32 pages, harvmac (b

On 3d N=8 Lorentzian BLG theory as a scaling limit of 3d superconformal N=6 ABJM theory

We elaborate on the suggestion made in arXiv:0806.3498 that the 3d \N=8 superconformal SU(N) Chern-Simons-matter theory of Lorentzian Bagger-Lambert-Gustavson type (L-BLG) can be obtained by a scaling limit (involving sending the level k to infinity and redefining the fields) from the \N=6 superconformal U(N)xU(N) Chern-Simons-matter theory of Aharony, Bergman, Jafferis and Maldacena (ABJM). We show that to implement such a limit in a consistent way one is to extend the ABJM theory by an abelian "ghost" multiplet. The corresponding limit at the 3-algebra level also requires extending the non-antisymmetric Bagger-Lambert 3-algebra underlying the ABJM theory by a negative-norm generator. We draw analogy with similar scaling limits discussed previously for bosonic Chern-Simons theory and comment on some implications of this relation between the ABJM and L-BLG theories.Comment: 16 pages; published version - reference added, minor correction

Chiral Symmetry Breaking from Intersecting D-Branes

We study a class of intersecting D-brane models in which fermions localized at different intersections interact via exchange of bulk fields. In some cases these interactions lead to dynamical symmetry breaking and generate a mass for the fermions. We analyze the conditions under which this happens as one varies the dimensions of the branes and of the intersections.Comment: 29 pages, harvmac (b

Holographic U(1)_A and String Creation

We analyze the resolution of the U(1)_A problem in the Sakai-Sugimoto holographic dual of large N_c QCD at finite temperature. It has been shown that in the confining phase the axial symmetry is broken at order 1/N_c, in agreement with the ideas of Witten and Veneziano. We show that in the deconfined phase the axial symmetry remains unbroken to all orders in 1/N_c. In this case the breaking is due to instantons which are described by spacelike D0-branes, in agreement with 'tHooft's resolution. The holographic dual of the symmetry breaking fermion condensate is a state of spacelike strings between the D0-brane and the flavor D8-branes, which result from a spacelike version of the string creation effect. In the intermediate phase of deconfinement with broken chiral symmetry the instanton gas approximation is possibly regulated in the IR, which would imply an eta' mass-squared of order exp(-N_c).Comment: 18 pages, 19 figures, minor change

Quark mass and condensate in HQCD

We extend the Sakai-Sugimoto holographic model of QCD (HQCD) by including the scalar bi-fundamental "tachyon" field in the 8-brane-anti-8-brane probe theory. We show that this field is responsible both for the spontaneous breaking of the chiral symmetry, and for the generation of (current algebra) quark masses, from the point of view of the bulk theory. As a by-product we show how this leads to the Gell-Mann- Oakes-Renner relation for the pion mass.Comment: 23 pages, 7 figures; v2: corrected typos in eqs. (4.3), (4.4), (4.5), (4.9) and (4.11), and corrected figures 3, 4, 5 and 6; v3: section 5.3 on the pion mass rewritten in a clearer way, version published in JHE

Holographic QCD and Pion Mass

To realize massive pions, we study variations of the holographic model of massless QCD using the D4/D8/anti-D8 brane configuration proposed by Sakai and Sugimoto. We propose deformations which break the chiral symmetry explicitly and compute the mass of the pions and vector mesons. The observed value of the pion mass can be obtained. We also argue a chiral perturbation corresponding to our deformation.Comment: 23pages, minor changes, references adde

Stringy NJL and Gross-Neveu models at finite density and temperature

Nonlocal stringy versions of the Nambu-Jona-Lasinio and Gross-Neveu models arise in a certain limit of holographic QCD. We analyze the phase structure at finite density and temperature at strong coupling in terms of probe branes in the gravity dual. Comparison with the phase structure of the local field theory models shows qualitative agreement with some aspects, and disagreement with others. Finally, we explain how to construct the Landau potentials for these models by taking the probe branes off-shell.Comment: 32 pages, uses JHEP3.cls; v2, references added, version to be submitted to JHE

On extending actions of groups

Problems of dense and closed extension of actions of compact transformation groups are solved. The method developed in the paper is applied to problems of extension of equivariant maps and of construction of equivariant compactifications