Deformations Of AdS Research Articles

Classifying Nearest-Neighbor Interactions and Deformations of AdS.

We classify all regular solutions of the Yang-Baxter equation of eight-vertex type. Regular solutions correspond to spin chains with nearest-neighbor interactions. We find a total of four independent solutions. Two are related to the usual six- and eight-vertex models that have R matrices of difference form. We find two new solutions of the Yang-Baxter equation, which are manifestly of nondifference form. These new solutions contain the S-matrices of the AdS_{2} and AdS_{3} integrable models as a special case. This can be used as a starting point to study and classify integrable deformations of these holographic integrable systems.

Yang-Mills supersymmetry and deformations of AdS5 × S5 solution with the Yang-Baxter equation

The Yang-Mills supersymmetry is considered using the Yang-Baxter equations as deformations of AdS5 × S5 in which they are substituted as a twist of the conformal Drinfeld algebra. The operators here are represented as Killing vectors. The solution of this problem is represented as the Θ-matrix for which the deformation φ was found, which is a super gravitational solution.

Holographic dual of the Ω -background

We find an explicit supergravity background dual to the $\Omega$-deformation of a four-dimensional $\mathcal{N}=2$ SCFT on $\mathbb{R}^4$. The solution can be constructed in the five-dimensional ${\cal N}=4^+$ gauged supergravity and has a nontrivial self-dual 2-form. When uplifted to type IIB supergravity the background is a deformation of AdS$_5\times S^5$ which preserves 16 supercharges. We also discuss generalizations of this solution corresponding to turning on a vacuum expectation value for a scalar operator in the dual SCFT.

Embedding the modified CYBE in supergravity

It has recently been demonstrated that given a generic solution, the Classical Yang–Baxter Equation (CYBE) emerges from supergravity via the open-closed string map, thus providing tangible evidence for the conjectured equivalence between supergravity equations of motion and the homogeneous CYBE. To date, study of this equivalence has largely been confined to the NS sector. In this work, we make two extensions. First, we revisit the transformation of the RR sector and clarify its precise role in the emergence of the CYBE. Secondly, we identify direct products of coset geometries as the only setting where the transformation permits embeddings of the modified CYBE. We illustrate our solution generating technique with deformations of AdS_3 times S^3 times M_4, where M_4 = T^4 (K3) and S^3 times S^1, and explicitly construct one and two-parameter integrable q-deformations that are solutions to generalised supergravity.

Local \u03b2-deformations and Yang-Baxter sigma model

Homogeneous Yang-Baxter (YB) deformation of AdS5 × S5 superstring is revisited. We calculate the YB sigma model action up to quadratic order in fermions and show that homogeneous YB deformations are equivalent to β-deformations of the AdS5 ×S5 background when the classical r-matrices consist of bosonic generators. In order to make our discussion clearer, we discuss YB deformations in terms of the double-vielbein formalism of double field theory. We further provide an O(10, 10)-invariant string action that reproduces the Green-Schwarz type II superstring action up to quadratic order in fermions. When an AdS background contains a non-vanishing H-flux, it is not straightforward to perform homogeneous YB deformations. In order to get any hint for such YB deformations, we study β-deformations of H-fluxed AdS backgrounds and obtain various solutions of (generalized) type II supergravity.

Supersymmetric solutions of the cosmological, gauged, \u2102 magic model

We construct supersymmetric solutions of theories of gauged mathcal{N} = 1, d = 5 supergravity coupled to vector multiplets with a U(1)R Abelian (Fayet-Iliopoulos) gauging and an independent SU(2) gauging associated to an SU(2) isometry group of the Real Special scalar manifold. These theories provide minimal supersymmetrizations of 5-dimensional SU(2) Einstein-Yang-Mills theories with negative cosmological constant. We consider a minimal model with these gauge groups and the “magic model” based on the Jordan algebra J3ℂ with gauge group SU(3) × U(1)R, which is a consistent truncation of maximal SO(6)-gauged supergravity in d = 5 and whose solutions can be embedded in Type IIB Superstring Theory. We find several solutions containing selfdual SU(2) instantons, some of which asymptote to AdS5 and some of which are very small, supersymmetric, deformations of AdS5. We also show how some of those solutions can be embedded in Romans’ SU(2) × U(1)-gauged half-maximal supergravity, which was obtained by Lu, Pope and Tran by compactification of the Type IIB Superstring effective action. This provides another way of uplifting those solutions to 10 dimensions.

Quantum deformations of the flat space superstring

We discuss a quantum deformation of the Green-Schwarz superstring on flat space, arising as a contraction limit of the corresponding deformation of AdS_5 x S^5. This contraction limit turns out to be equivalent to a previously studied limit that yields the so-called mirror model - the model obtained from the light cone gauge fixed AdS_5 x S^5 string by a double Wick rotation. Reversing this logic, the AdS_5 x S^5 superstring is the double Wick rotation of a quantum deformation of the flat space superstring. This quantum deformed flat space string realizes symmetries of timelike kappa-Poincare type, and is T dual to dS_5 x H^5, indicating interesting relations between symmetry algebras under T duality. Our results directly extend to AdS_2 x S^2 x T^6 and AdS_3 x S^3 x T^4, and beyond string theory to many (semi)symmetric space coset sigma models, such as for example a deformation of the four dimensional Minkowski sigma model with timelike kappa-Poincare symmetry. We also discuss possible null and spacelike deformations.

Beta function of k deformed AdS5 × S 5 string theory

We calculate the one loop beta function for the would-be marginal coupling on the world sheet of the k deformed sigma models associated to a quantum group with q=exp(i pi/k). This includes the bosonic principal chiral models and symmetric space sigma models but also the k deformed semi-symmetric space sigma model describing strings in a deformation of AdS_5 x S^5. The world sheet sigma model is a current-current deformation of the gauged WZW model for the supergroup PSU(2,2|4) with level k. In the string theory context the beta function is shown to vanish because of the vanishing of the Killing form of PSU(2,2|4) which is another piece of evidence that the k deformed theories define consistent string theories.

Schrödinger holography with z = 2

We investigate holography for asymptotically Schrödinger spacetimes, using a frame formalism based on the anisotropic scaling symmetry. We build on our previous work on to propose a dictionary for z = 2. For z = 2, the scaling symmetry does not act on the additional null direction, which implies that in our dictionary it does not correspond to one of the field theory directions. This is significantly different from previous analyses based on viewing Schrödinger as a deformation of AdS. We study this dictionary in the linearized theory and in an asymptotic expansion. We show that a solution exists in an asymptotic expansion for arbitrary sources for the relevant operators in the stress energy complex.

On deformations of AdS n × S n supercosets

We study the deformed AdS 5 × S 5 supercoset model of arXiv:1309.5850 which depends on one parameter κ and has classical quantum group symmetry. We confirm the conjecture that in the “maximal” deformation limit, κ → ∞, this model is T-dual to “flipped” double Wick rotation of the target space AdS 5 × S 5, i.e. dS 5 × H 5 space supported by an imaginary 5-form flux. In the imaginary deformation limit, κ → i, the corresponding target space metric is of a pp-wave type and thus the resulting light-cone gauge S-matrix becomes relativistically invariant. Omitting non-unitary contributions of imaginary WZ terms, we find that this tree-level S-matrix is equivalent to that of the generalized sine-Gordon model representing the Pohlmeyer reduction of the undeformed AdS 5 × S 5 superstring model. We also study in some detail similar deformations of the AdS 3 × S 3 and AdS 2 × S 2 supercosets. The bosonic part of the deformed AdS 3 × S 3 model happens to be equivalent to the symmetric case of the sum of the Fateev integrable deformation of the SL(2) and SU(2) principal chiral models, while in the AdS 2 × S 2 case the role of the Fateev model is played by the 2d “sausage” model. The κ = i limits are again directly related to the Pohlmeyer reductions of the corresponding AdS n × S n supercosets: (2,2) super sine-Gordon model and its complex sine-Gordon analog. We also discuss possible deformations of AdS 3 × S 3 with more than one parameter.

PROBING THE 5TH DIMENSION WITH THE QCD STRING

A salient feature of String/Gauge duality is an extra 5th dimension. Here we study the effect of confining deformations of AdS5 and compute the spectrum of a string stretched between infinitely massive quarks and compare it with the quantum states of the QCD flux as determined by Kuti, Juge and Morningstar in lattice simulations. In the long flux tube limit the AdS string probes the metric near the IR cutoff of the 5th dimension with a spectrum approximated by a Nambu-Goto string in 4-d flat space, whereas at short distance the string moves to the UV region with a discrete spectrum for pure AdS5. We also review earlier results on glueballs states and the cross-over between hard and soft diffractive scattering that support this picture.

D7 Brane Embeddings and Chiral Symmetry Breaking

We study the embedding of D7 brane probes in five geometries that are deformations of AdS_5 x S^5. Each case corresponds to the inclusion of quark fields in a dual gauge theory where we are interested in investigating whether chiral symmetry breaking occurs. We use a supersymmetric geometry describing an N=2 theory on its moduli space and a dilaton driven non-supersymmetric flow to establish criteria for a chiral symmetry breaking embedding. We develop a simple spherical D7 embedding that tests the repulsion of the core of the geometry and signals dynamical symmetry breaking. We then use this tool in more complicated geometries to show that an N=2* theory and a non-supersymmetric theory with scalar masses do not induce a chiral condensate. Finally we provide evidence that the Yang Mills* geometry does.

A deformation of AdS5 × S5

We analyse a one-parameter family of supersymmetric solutions of type IIB supergravity that includes AdS5 × S5. For small values of the parameter the solutions are causally well behaved, but beyond a critical value closed timelike curves (CTCs) appear. The solutions are holographically dual to supersymmetric Yang–Mills theory on a non-conformally flat background with non-vanishing R-currents. We compute the holographic energy–momentum tensor for the spacetime and show that it remains finite even when the CTCs appear. The solutions, as well as the uplift of some recently discovered AdS5 black-hole solutions, are shown to preserve precisely two supersymmetries.

Boundary fluctuations of AdS string

We analyse the world-sheet perturbations of string theory formulated around AdS 3 background. We identify a set of operators that, while added to the world-sheet action, generate the boundary fluctuations of AdS 3. The effect of these operators can be collectively defined in terms of Liouville field living on the AdS 3 boundary. We then study various deformations of AdS 3 generated by boundary fluctuations by turning on suitable world-sheet couplings. We also discuss certain small fluctuations around the BTZ black hole.