Gianluca Grignani

The SU(2) x SU(2) sector in the string dual of N=6 superconformal Chern-Simons theory

We examine the string dual of the recently constructed N=6 superconformal Chern–Simons theory of Aharony, Bergman, Jafferis and Maldacena (ABJM theory). We focus in particular on the SU(2)×SU(2) sector. We find a sigma-model limit in which the resulting sigma-model is two Landau–Lifshitz models added together. We consider a Penrose limit for which we can approach the SU(2)×SU(2) sector. Finally, we find a new Giant Magnon solution in the SU(2)×SU(2) sector corresponding to one magnon in each SU(2). We put these results together to find the full magnon dispersion relation and we compare this to recently found results for ABJM theory at weak coupling.

Finite size Giant Magnons in the string dual of N=6 superconformal Chern-Simons theory

We find the exact solution for a finite size Giant Magnon in the SU(2) × SU(2) sector of the string dual of the = 6 superconformal Chern-Simons theory recently constructed by Aharony, Bergman, Jafferis and Maldacena. The finite size Giant Magnon solution consists of two magnons, one in each SU(2). In the infinite size limit this solution corresponds to the Giant Magnon solution of arXiv:0806.4959. The magnon dispersion relation exhibits finite-size exponential corrections with respect to the infinite size limit solution.

Gauge invariant finite size spectrum of the giant magnon

It is shown that the finite size corrections to the spectrum of the giant magnon solution of classical string theory, computed using the uniform light-cone gauge, are gauge invariant and have physical meaning. This is seen in two ways: from a general argument where the single magnon is made gauge invariant by putting it on an orbifold as a wrapped state obeying the level matching condition as well as all other constraints, and by an explicit calculation where it is shown that physical quantum numbers do not depend on the uniform light-cone gauge parameter. The resulting finite size effects are exponentially small in the R-charge and the exponent (but not the prefactor) agrees with gauge theory computations using the integrable Hubbard model.

Heating up the BIon

We propose a new method to consider D-brane probes in thermal backgrounds. The method builds on the recently developed blackfold approach to higher-dimensional black holes. While D-brane probes in zero-temperature backgrounds are well-described by the Dirac-Born-Infeld (DBI) action, this method addresses how to probe thermal backgrounds. A particularly important feature is that the probe is in thermal equilibrium with the background. We apply our new method to study the thermal generalization of the BIon solution of the DBI action. The BIon solution is a configuration in flat space of a D-brane and a parallel anti-D-brane connected by a wormhole with F-string charge. In our thermal generalization, we put this configuration in hot flat space. We find that the finite temperature system behaves qualitatively different than its zero-temperature counterpart. In particular, for a given separation between the D-brane and anti-D-brane, while at zero temperature there are two phases, at finite temperature there are either one or three phases available.

Thermodynamics of the hot BIon

Abstract We investigate the thermodynamics of the recently obtained finite temperature BIon solution of [G. Grignani, T. Harmark, A. Marini, N.A. Obers, M. Orselli, Heating up the BIon, arXiv:1012.1494 [hep-th] ], focusing on two aspects. The first concerns comparison of the free energy of the three available phases for the finite-temperature brane–antibrane–wormhole configuration. Based on this we propose a heuristic picture for the dynamics of the phases that involves a critical temperature below which a stable phase exists. This stable phase is the finite temperature analogue of the thin throat branch of the extremal brane–antibrane–wormhole configuration. The second aspect that we consider is the possibility of constructing a finite temperature generalization of the infinite spike configuration of the extremal BIon. To this end we identify a correspondence point at the end of the throat where the thermodynamics of the D3–F1 blackfold configuration can be matched to that of k non-extremal black fundamental strings.

A new rolling tachyon solution of cubic string field theory

We present a new analytic time dependent solution of cubic string field theory at the lowest order in the level truncation scheme. The tachyon profile we have found is a bounce in time, a C ∞ function which represents an almost exact solution, with an extremely good degree of accuracy, of the classical equations of motion of the truncated string field theory. Such a finite energy solution describes a tachyon which at x 0 = -∞ is at the maximum of the potential, at later times rolls toward the stable minimum and then up to the other side of the potential toward the inversion point and then back to the unstable maximum for x 0 → +∞. The energy-momentum tensor associated with this rolling tachyon solution can be explicitly computed. The energy density is constant, the pressure is an even function of time which can change sign while the tachyon rolls toward the minimum of its potential. A new form of tachyon matter is realized which might be relevant for cosmological applications.

The superstring Hagedorn temperature in a pp-wave background

The thermodynamics of type-IIB superstring theory in the maximally supersymmetric plane wave background is studied. We compute the thermodynamic partition function for non-interacting strings exactly and the result differs slightly from previous computations. We clarify some of the issues related to the Hagedorn temperature in the limits of small and large constant RR 5-form. We study the thermodynamic behavior of strings in the case of AdS3 × S3 × T4 geometries in the presence of NS-NS and RR 3-form backgrounds. We also comment on the relationship of string thermodynamics and the thermodynamic behavior of the sector of Yang-Mills theory which is the holographic dual of the string theory.

Finite-size corrections for quantum strings on {\text{Ad}}{{\text{S}}_4} \times \mathbb{C}{P^3}

We revisit the calculation of curvature corrections to the pp-wave energy of type IIA string states on

Full Lagrangian and Hamiltonian for quantum strings on AdS4 × CP3 in a near plane wave limit

{\text{Ad}}{{\text{S}}_4} \times \mathbb{C}{P^3}

Thermodynamic partition function of matrix superstrings

initiated in arXiv:0807.1527. Using the near pp-wave Hamiltonian found in arXiv:0912.2257, we compute the first non-vanishing correction to the energy of a set of bosonic string states at order 1/R2, where R is the curvature radius of the background. The leading curvature corrections give rise to cubic, order 1/R, and quartic, order 1/R2, terms in the Hamiltonian, for which we implement the appropriate normal ordering prescription. Including the contributions from all possible fermionic and bosonic string states, we find that there exist logarithmic divergences in the sums over mode numbers which cancel between the cubic and quartic Hamiltonian. We show that from the form of the cubic Hamiltonian it is natural to require that the cutoff for summing over heavy modes must be twice the one for light modes. With this prescription the strong-weak coupling interpolating function h(λ), entering the magnon dispersion relation, does not receive a one-loop correction, in agreement with the algebraic curve spectrum. However, the single magnon dispersion relation exhibits finite-size exponential corrections.