Narrow Results

We discuss the Penrose limit of the classical string geometry obtained from a truly marginal deformation of SL(2) ⊗ SU(2) WZNW model.

We present a new class of time-dependent solution to the ten-dimensional type 0 effective action. Given a generic potential of tachyon field, there exist phases where tachyon is either frozen at local extremals or free to propagate along flat directions. In the latter phase, a cosmology model is proposed where the tachyon plays the role of time.

In planar supersymmetric Yang–Mills theory we have studied one kind of (locally) BPS Wilson loops composed of a large number of light-like segments, i.e. null zig-zags. These contours oscillate around smooth underlying spacelike paths. At one-loop in perturbation theory, we have compared the finite part of the expectation value of null zig-zags to the finite part of the expectation value of non-scalar-coupled Wilson loops whose contours are the underlying smooth spacelike paths. In arXiv:0710.1060 [hep-th] it was argued that these quantities are equal for the case of a rectangular Wilson loop. Here we present a modest extension of this result to zig-zags of circular shape and zig-zags following non-parallel, disconnected line segments and show analytically that the one-loop finite part is indeed that given by the smooth spacelike Wilson loop without coupling to scalars which the zig-zag contour approximates. We make some comments regarding the generalization to arbitrary shapes.

We consider circular spinning string solutions in AdS₅×T^{1, 1} and calculate the quantum corrections to the energy at one-loop on worldsheet. The fluctuations are given as a set of harmonic oscillators and we calculate their normal mode frequency in closed form. The sum of frequency is equal to the one-loop string energy, which through AdS/CFT correspondence corresponds to the leading order correction of the conformal dimension for long operators in Klebanov–Witten conifold gauge field theory.

Recently there has been progress on the computation of two- and three-point correlation functions with two "heavy" states via semiclassical methods. We extend this analysis to the case of AdS₅×T^{1, 1}, and examine the suggested procedure for the case of several simple string solutions. By making use of AdS/CFT duality, we derive the relevant correlation functions of operators belonging to the dual gauge theory.

We consider general supersymmetric Wilson loops in ABJM model, which is Chern–Simons-matter theory in (2+1) dimensions with 𝒩 = 6 supersymmetry. The Wilson loops of our interest are so-called Zarembo-type: they have generic contours in spacetime, but the scalar field coupling is arranged accordingly so that there are unbroken supersymmetries. Following the supermatrix construction of Wilson loops by Drukker and Trancanelli and the generalization by Griguolo et al., we study 1/6-BPS Wilson loops and check that their expectation value is protected using perturbation up to two loops. We also study the dual string configuration in AdS₄×ℂℙ³ background and check the supersymmetry.

We study the gravity duals of striped holographic superconductors in the AdS black hole and AdS soliton backgrounds. We show the dependences of the condensation and the critical temperature/critical chemical potential on the inhomogeneity in these two different spacetimes. By exploring the dynamics of the normal phase through the scalar field perturbation, we argue that the pair susceptibility and the conductivity can be possible phenomenological indications to disclose the property of inhomogeneity.

The first run of the LHC has been tremendously successful, having discovered the Higgs boson as well as having set stringent limits on superpartner masses. This has severely constrained supersymmetric models. A consistent scenario based on LHC data suggests that the third generation sfermions, Higgsinos and the gluino must be light while the first two generation sfermions are heavy. Furthermore, an extra contribution to the Higgs quartic coupling is needed to explain the 126 GeV Higgs mass. Interestingly this spectrum can naturally arise from supersymmetry breaking in a warped geometry where the sfermion spectrum is related to the fermion mass hierarchy. Various possible scenarios are reviewed and compared with the data from the first run at the LHC.

A metric is proposed to explore the noncommutative form of the anti-de Sitter (AdS) space due to quantum effects. It has been proved that the noncommutativity in AdS space induces a single component gravitoelectric field. The holographic Ryu–Takayanagi (RT) algorithm is then applied to compute the entanglement entropy (EE) in dual CFT₂. This calculation can be exploited to compute ultraviolet–infrared (UV–IR) cutoff dependent central charge of the certain noncommutative CFT₂. This noncommutative computation of the EE can be interpreted in the form of the surface/state correspondence. We have shown that noncommutativity increases the dimension of the effective Hilbert space of the dual conformal field theory (CFT).

The ${𝒩}=4$ superconformal algebra is derived from the symmetry transformations of fields in the ${𝒩}=4$ SYM action in $D=4$. We use a Majorana–Weyl spinor in $D=10$ instead of four Weyl spinors in $D=4$. This makes it transparent to relate generators of the ${𝒩}=4$ superconformal algebra to those of the super-${\mathrm{\text{AdS}}}_5\times {\mathrm{\text{S}}}^5$ algebra. Especially, we obtain the concrete map from the supersymmetries $Q$ and conformal supersymmetries $S$ in ${𝒩}=4$ SYM to the supersymmetries $({{𝒬}}_1,{{𝒬}}_2)$ in the ${\mathrm{\text{AdS}}}_5\times {\mathrm{\text{S}}}^5$ background.

The Schwinger effect in the presence of instantons and background magnetic field was considered to study the dependence of critical electric field on instanton density and magnetic field using AdS/CFT conjecture. The gravity side is the near horizon limit of D3$-$D(−1) background with electric and magnetic fields on the brane. Our approach is based on the potential analysis for particle–antiparticle pair at zero and finite temperatures, where the zero temperature case is a semi-confining theory. We find that presence of instantons suppresses the pair creation effect, similar to a background magnetic field. Then, the production rate will be obtained numerically using the expectation value of circular Wilson loop. The obtained production rate in a magnetic field is in agreement with previous results.

We provide a brief summary of a method to calculate improvements to the Veneziano amplitude, creating sub-leading nonlinearities in the Regge trajectory of states. We formulate it as an extension of a computation by Makeenko and Olesen. We begin in a confining gauge theory coupled to matter, rewriting the meson scattering amplitude as a specific path integral over shapes and sizes of closed Wilson loops using the worldline formalism. We then prescribe how to further the computation at strong coupling by employing holography, which provides a prescription for the expectation value of these Wilson loops in strongly coupled regimes. The computation we desire then appears to subsume to a certain calculation in the effective field theory of a string worldsheet embedded in a certain broad class of allowed holographic backgrounds. A convenient interaction picture presents itself naturally in this context, allowing us to draw Feynman diagrams corresponding to the first few corrections due to weaker coupling regimes. The answer we find has qualitatively the same features as other endeavors with the same objective.

Scalar fields on the bulk side of AdS/CFT correspondence can be assigned unconventional boundary conditions related to the conventional one by Legendre transform. One can further perform double trace deformations which relate the two boundary conditions via renormalization group flow. Thinking of these operators as S and T transformations, respectively, we explore the SL(2, R) family of models which naively emerges from repeatedly applying these operations. Depending on the parameters, the effective masses vary and can render the theory unstable. However, unlike in the SL(2, Z) structure previously seen in the context of vector fields in AdS₄, some of the features arising from this exercise, such as the vacuum susceptibility, turns out to be scheme dependent. We explain how scheme independent physical content can be extracted in spite of some degree of scheme dependence in certain quantities.

In this paper, we examine some structural aspects of the AdS/CFT such as the way of obtaining the expectation value of product of operators of the CFT, and ideas that should be considered when a proof of AdS/CFT is under consideration.

In earlier work, the evolution operator for the exact RG equation was mapped to a field theory in Euclidean AdS. This gives a simple way of understanding AdS/CFT. We explore aspects of this map by studying a simple example of a Schrödinger equation for a free particle with time-dependent mass. This is an analytic continuation of an ERG like equation. We show for instance that it can be mapped to a harmonic oscillator. We show that the same techniques can lead to an understanding of dS/CFT too.

In this paper, we study two-point correlation function in a medium composed of two kinds of matter, which is the dual of a three-dimensional generalized p-brane gas geometry. Following the holographic prescription, we calculate temporal and spatial two-point functions in the medium. In general, the screening effect of the medium makes two-point functions decreases more rapidly than the CFTs two-point function. In the extremal limit, however, we find that a temporal two-point function is still conformal. This indicates that a two-dimensional UV CFT flows into a one-dimensional quantum mechanics in the IR limit. This is consistent with the fact that the near horizon geometry in the extremal limit reduces to AdS₂. We also investigate holographic mutual information representing the correlation between two subsystems. We show that a critical distance in the IR region, where the mutual information vanishes, leads to a similar behavior to the correlation length of a two-point function.

We study a class of solutions to the SL(2, ℝ)_k Knizhnik–Zamolodchikov equation.

First, logarithmic solutions which represent four-point correlation functions describing string scattering processes on three-dimensional anti-de Sitter space are discussed. These solutions satisfy the factorization ansatz and include logarithmic dependence on the SL(2, ℝ)-isospin variables. Different types of logarithmic singularities arising are classified and the interpretation of these is discussed. The logarithms found here fit into the usual pattern of the structure of four-point function of other examples of AdS/CFT correspondence. Composite states arising in the intermediate channels can be identified as the phenomena responsible for the appearance of such singularities in the four-point correlation functions. In addition, logarithmic solutions which are related to nonperturbative (finite k) effects are found.

By means of the relation existing between four-point functions in Wess–Zumino–Novikov–Witten model formulated on SL(2, ℝ) and certain five-point functions in Liouville quantum conformal field theory, we show how the reflection symmetry of Liouville theory induces particular ℤ₂ symmetry transformations on the WZNW correlators. This observation allows to find relations between different logarithmic solutions. This Liouville description also provides a natural explanation for the appearance of the logarithmic singularities in terms of the operator product expansion between degenerate and puncture fields.

We review and extend the progress made over the past few years in understanding the structure of toric quiver gauge theories; those which are induced on the worldvolume of a stack of D3-branes placed at the tip of a toric Calabi–Yau cone, at an "orbifold point" in Kähler moduli space. These provide an infinite class of four-dimensional superconformal field theories which may be studied in the context of the AdS/CFT correspondence. It is now understood that these gauge theories are completely specified by certain two-dimensional torus graphs, called brane tilings, and the combinatorics of the dimer models on these graphs. In particular, knowledge of the dual Sasaki–Einstein metric is not required to determine the gauge theory, only topological and symplectic properties of the toric Calabi–Yau cone. By analyzing the symmetries of the toric quiver theories we derive the dimer models and use them to construct the moduli space of the theory both classically and semiclassically. Using mirror symmetry the brane tilings are shown to arise in string theory on the worldvolumes of the fractional D6-branes that are mirror to the stack of D3-branes at the tip of the cone.

We review the holographic duals of gauge theories with eight supercharges obtained by adding very few flavors to pure supersymmetric Yang–Mills with 16 supercharges. Assuming a brane-probe limit, the gravity duals are engineered in terms of probe branes (the so-called flavor brane) in the background of the color branes. Both types of branes intersect on a given subspace in which the matter is confined. The gauge theory dual is thus the corresponding flavoring of the gauge theory with 16 supercharges. Those theories have in general a nontrivial phase structure; which is also captured in a beautiful way by the gravity dual. Along the lines of the gauge/gravity duality, we review also some of the results on the meson spectrum in the different phases of the theories.

We find new explicit solutions describing closed strings spinning with equal angular momentum in two independent planes in the AdS₅ black hole space–time. These are 2n-folded strings in the radial direction and also winding m times around an angular direction. We specially consider these solutions in the long string and high temperature limit, where it is shown that there is a logarithmic correction to the scaling between energy and spin. This is similar to the one-spin case. The strings are spinning, or actually orbiting around the black hole of the AdS₅ black hole space–time, similar to the solutions previously found in black hole space–times.