Planckian AdS2×S2AdS_2 \times S_2 space is an exact solution of the semiclassical Einstein equations

The product space configuration $AdS_2\times S_2$ (with $l$ and $r$ being radiuses of the components) carrying the electric charge $Q$ is demonstrated to be an exact solution of the semiclassical Einstein equations in presence of the Maxwell field. If the logarithmic UV divergences are absent in the four-dimensional theory the solution we find is identical to the classical Bertotti-Robinson space ($r=l=Q$) with no quantum corrections added. In general, the analysis involves the quadratic curvature coupling $\lambda$ appearing in the effective action. The solutions we find are of the following types: i) (for arbitrary $\lambda$) charged configuration which is quantum deformation of the Bertotti-Robinson space; ii) ($\lambda >\lambda_{cr}$) Q=0 configuration with $l$ and $r$ being of the Planck order; iii) ($\lambda<\lambda_{cr}$) $Q\neq 0$ configuration ($l$ and $r$ are of the Planck order) not connected analytically to the Bertotti-Robinson space. The interpretation of the solutions obtained and an indication on the internal structure of the Schwarzschild black hole are discussed.Comment: 14 pages, latex, 1 figure; v2: a note on S2*S2 type solutions adde

Puzzles of eta-deformed AdS_5 x S^5

We derive the part of the Lagrangian for the sigma model on the eta-deformed AdS_5 x S^5 space which is quadratic in fermions and has the full dependence on bosons. We then show that there exists a field redefinition which brings the corresponding Lagrangian to the standard form of type IIB Green-Schwarz superstring. Reading off the corresponding RR couplings, we observe that they fail to satisfy the supergravity equations of motion, despite the presence of kappa-symmetry. However, in a special scaling limit our solution reproduces the supergravity background found by Maldacena and Russo. Further, using the fermionic Lagrangian, we compute a number of new matrix elements of the tree level world-sheet scattering matrix. We then show that after a unitary transformation on the basis of two-particle states which is not one-particle factorisable, the corresponding T-matrix factorises into two equivalent parts. Each part satisfies the classical Yang-Baxter equation and coincides with the large tension limit of the q-deformed S-matrix.Comment: 59 pages, 1 figure, v2: minor correction

Five-loop Konishi from the Mirror TBA

We use the Thermodynamic Bethe Ansatz equations for the AdS_5 \times S^5 mirror model to derive the five-loop anomalous dimension of the Konishi operator. We show numerically that the corresponding result perfectly agrees with the one recently obtained via the generalized Luscher formulae. This constitutes an important test of the AdS/CFT TBA system.Comment: 14 pages, 2 figures, v2: published versio

Towards 4-point correlation functions of any 1/2-BPS operators from supergravity

The quartic effective action for Kaluza-Klein modes that arises upon compactification of type IIB supergravity on the five-sphere S^5 is a starting point for computing the four-point correlation functions of arbitrary weight 1/2-BPS operators in N=4 super Yang-Mills theory in the supergravity approximation. The apparent structure of this action is rather involved, in particular it contains quartic terms with four derivatives which cannot be removed by field redefinitions. By exhibiting intricate identities between certain integrals involving spherical harmonics of S^5 we show that the net contribution of these four-derivative terms to the effective action vanishes. Our result is in agreement with and provides further support to the recent conjecture on the Mellin space representation of the four-point correlation function of any 1/2-BPS operators in the supergravity approximation.Comment: 12 page

TT‾T\overline{T} Deformations of nonrelativistic models

The light-cone gauge approach to $T\overline{T}$ deformed models is used to derive the $T\overline{T}$ deformed matrix nonlinear Schr\"odinger equation, the Landau--Lifshitz equation, and the Gardner equation. Properties of one-soliton solutions of the $T\overline{T}$ deformed nonlinear Schr\"odinger and Korteweg--de Vries equations are discussed in detail. The NLS soliton exhibits the recently discussed phenomenon of widening/narrowing width of particles under the $T\overline{T}$ deformation. However, whether the soliton's size is increasing or decreasing depends not only on the sign of the deformation parameter but also on soliton and potential parameters. The $T\overline{T}$ deformed KdV equation admits a one-parameter family of one-soliton solutions in addition to the usual velocity parameter. The extra parameter modifies the properties of the soliton, in particular, it appears in the dispersion relation.Comment: 34 pages, many figures. V2: minor corrections. V3: Two new comment sections added, accepted for publication in JHE