Marija Zamaklar

Finite-size effects from giant magnons

In order to analyze finite-size effects for the gauge-fixed string sigma model on AdS5 × S 5 , we construct one-soliton solutions carrying finite angular momentum J . In the infinite J limit the solutions reduce to the recently constructed one-magnon configuration of Hofman and Maldacena. The solutions do not satisfy the level-matching condition and hence exhibit a dependence on the gauge choice, which however disappears as the size J is taken to infinity. Interestingly, the solutions do not conserve all the global charges of the psu(2, 2|4) algebra of the sigma model, implying that the symmetry algebra of the gauge-fixed string sigma model is different from psu(2, 2|4) for finite J , once one gives up the level-matching condition. The magnon dispersion relation exhibits exponential corrections with respect to the infinite J solution. We also find a generalisation of our one-magnon configuration to a solution carrying two charges on the sphere. We comment on the possible implications of our findings for the existence of the Bethe ansatz describing the spectrum of strings carrying finite charges.

The Zamolodchikov-Faddeev Algebra for AdS5 x S5 Superstring

We discuss the Zamolodchikov-Faddeev algebra for the superstring sigma-model on AdS5 ×S 5 . We find the canonical su(2|2) 2 invariant S-matrix satisfy- ing the standard Yang-Baxter and crossing symmetry equations. Its near-plane-wave expansion matches exactly the leading order term recently obtained by the direct per- turbative computation. We also show that the S-matrix obtained by Beisert in the gauge theory framework does not satisfy the standard Yang-Baxter equation, and, as a consequence, the corresponding ZF algebra is twisted. The S-matrices in gauge and string theories however are physically equivalent and related by a non-local transformation of the basis states which is explicitly constructed.

Holographic melting and related properties of mesons in a quark-gluon plasma

We analyze mesons at finite temperature in a chiral, confining string dual. The temperature dependence of low-spin as well as high-spin meson masses is shown to exhibit a pattern familiar from the lattice. Furthermore, we find the dissociation temperature of mesons as a function of their spin, showing that at a fixed quark mass, mesons with larger spins dissociate at lower temperatures. The Goldstone bosons associated with chiral symmetry breaking are shown to disappear above the chiral symmetry restoration temperature. Finally, we show that holographic considerations imply that large-spin mesons do not experience drag effects when moving through the quark-gluon plasma. They do, however, have a maximum velocity for fixed spin, beyond which they dissociate.

The off-shell symmetry algebra of the light-cone AdS5x S5 superstring

We analyze the psu(2,2|4) supersymmetry algebra of a superstring prop- agating in the AdS5 × S 5 background in the uniform light-cone gauge. We consider the off-shell theory by relaxing the level-matching condition and take the limit of infinite light-cone momentum, which decompactifies the string world-sheet. We fo- cus on the psu(2|2) ⊕ psu(2|2) subalgebra which leaves the light-cone Hamiltonian invariant and show that it undergoes extension by a central element which is ex- pressed in terms of the level-matching operator. This result is in agreement with the conjectured symmetry algebra of the dynamic S-matrix in the dual N = 4 gauge theory.

The AdS5xS5 Superstring in Light-Cone Gauge and its Bethe Equations

We use the uniform light-cone gauge to derive an exact gauge-fixed Lagrangian and light-cone Hamiltonian for the Green–Schwarz superstring in AdS5 × S5. We then quantize the theory perturbatively in the near plane wave limit, and compute the leading 1/J correction to a generic string state from the rank-1 subsectors. These investigations enable us to propose a new set of light-cone Bethe equations for the quantum string. The equations have a simple form and yield the correct spinning string and flat space limits. Finally, we clarify the notion of closed sectors in string theory by proving the existence of perturbative effective string Hamiltonians which are direct analogues of (all-loop) dilatation operators in the dual N = 4 gauge theory.

Quantum corrections to spinning strings in AdS5xS5 versus Bethe ansatz: a comparative study

We analyze quantum corrections to rigid spinning strings in AdS5 × S5. The one-loop worldsheet quantum correction to the string energy is compared to the finite-size correction from the quantum string Bethe ansatz. Expanding the summands of the string theory energy shift in the parameter 1/2 and subsequently resumming them yields a divergent result. However, upon zeta-function regularisation these results agree with the Bethe ansatz in the first three orders. We also perform an analogous computation in the limit of large winding number, which results in a disagreement with the string Bethe ansatz prediction. A similar mismatch is observed numerically. We comment on the possible origin of this discrepancy.

Stringy sums and corrections to the quantum string Bethe ansatz

We analyze the effects of zeta-function regularization on the evaluation of quantum corrections to spinning strings. Previously, this method was applied in the sl(2) subsector and yielded agreement to third order in perturbation theory with the quantum string Bethe ansatz. In this note we discuss related sums and compare zeta-function reg- ularization against exact evaluation of the sums, thereby showing that the zeta-function regularized expression misses out perturbative as well as non-perturbative terms. In par- ticular, this may imply corrections to the proposed quantum string Bethe equations. This also explains the previously observed discrepancy between the semi-classical string and the quantum string Bethe ansatz in the regime of large winding number.

How accurate is the quantum string Bethe ansatz

We compare solutions of the quantum string Bethe equations with explicit one-loop calculations in the sigma-model on AdS5 × S^5. The Bethe ansatz exactly reproduces the spectrum of infinitely long strings. When the length is finite, we find that deviations from the exact answer arise which are exponentially small in the string length.

Supergravity solutions for D-branes in Hpp-wave backgrounds

We derive two families of supergravity solutions describing D-branes in the maximally supersymmetric Hpp-wave background. The first family of solutions corresponds to quarter-BPS D-branes. These solutions are delocalised along certain directions transverse to the pp-wave. The second family corresponds to the non-supersymmetric D-branes. These solutions are fully localised. A peculiar feature of the nonsupersymmetric solutions is that gravity becomes repulsive close to the core of the D-brane. Both families preserve the amount of supersymmetry predicted by the D-brane probe/CFT analysis. All solutions are written in Brinkman coordinates. To construct these kind of solutions it is crucial to identify the coordinates in which the ansatz looks the simplest. We argue that the natural coordinates to get the supergravity description of the half-BPS branes are the Rosen coordinates.We derive two families of supergravity solutions describing D-branes in the maximally supersymmetric Hpp-wave background. The first family of solutions corresponds to quarter-BPS D-branes. These solutions are delocalized along certain directions transverse to the pp-wave. The second family corresponds to the non-supersymmetric D-branes. These solutions are fully localized. A peculiar feature of the non-supersymmetric solutions is that gravity becomes repulsive close to the core of the D-brane. Both families preserve the amount of supersymmetry predicted by the D-brane probe/CFT analysis. All solutions are written in Brinkman coordinates. To construct these kinds of solutions it is crucial to identify the coordinates in which the ansatz looks the simplest. We argue that the natural coordinates to get the supergravity description of the half-BPS branes are the Rosen coordinates.

D-branes in a plane wave from covariant open strings

We derive boundary conditions for the covariant open string corresponding to D-branes in an Hpp-wave by requiring kappa-symmetry of its bulk action. Both half-supersymmetric and quarter-supersymmetric branes are seen to arise in this way, and the analysis furthermore agrees fully with the existing probe brane and supergravity computations. We elaborate on the origin of dynamical and kinematical supersymmetries from the covariant point of view. In particular we focus on the D-string which only preserves half of the dynamical supersymmetries and none of the kinematical ones. We discuss its origin in AdS5×S5 and its world-volume spectrum.