We study a GKP-like classical string solution on a q-deformed AdS_5 x S^5 background and argue the spacetime structure by using it as a probe. The solution cannot stretch beyond the singularity surface and this result may suggest that the holographic relation is realized inside the singularity surface. This observation leads us to introduce a new coordinate system which describes the spacetime only inside the singularity surface. With the new coordinate system, we study minimal surfaces and derive a deformed Neumann-Rosochatius system with a rigid string ansatz.
We study minimal surfaces with a single cusp in a $q$-deformed AdS$_5\times$S$^5$ background. The cusp is composed of two half-lines with an arbitrary angle and is realized on a surface specified in the deformed AdS$_5$. The classical string solutions attached to this cusp are regarded as a generalization of configurations studied by Drukker and Forini in the undeformed case. By taking an antiparallel-lines limit, a quark-antiquark potential for the $q$-deformed case is derived with a certain subtraction scheme. The resulting potential becomes linear at short distances with a finite deformatio…
In this thesis we discuss how one can derive the quantum spectral curve for the $η$-deformed AdS$_5 \times S^5$ superstring, an integrable deformation of the AdS$_5 \times $S$^5$ superstring with quantum group symmetry. This model can be viewed as a trigonometric version of the AdS$_5 \times $S$^5$ superstring, like the Heisenberg xxz spin chain is a trigonometric version of the xxx spin chain. Our derivation starts from the ground-state thermodynamic Bethe ansatz equations and discusses the construction of both the undeformed and the $η$-deformed quantum spectral curve. We reformulate it firs…
We show that bosonic spinning strings on the η-deformed AdS_5 x S^5 background are naturally described as periodic solutions of a novel finite-dimensional integrable system which can be viewed as a deformation of the celebrated Neumann model. For this deformed model we find the Lax representation and the analogue of the Uhlenbeck integrals.
The spectral problem for the ${\rm AdS}_5\times {\rm S}^5$ superstring and its dual planar maximally supersymmetric Yang-Mills theory can be efficiently solved through a set of functional equations known as the quantum spectral curve. We discuss how the same concepts apply to the $η$-deformed ${\rm AdS}_5\times {\rm S}^5$ superstring, an integrable deformation of the ${\rm AdS}_5\times {\rm S}^5$ superstring with quantum group symmetry. This model can be viewed as a trigonometric version of the ${\rm AdS}_5\times {\rm S}^5$ superstring, like the relation between the XXZ and XXX spin chains, or…
In this paper, we study the spin chain and string excitation in the two-parameters $q$-deformed AdS$_3\times$S$^3$ proposed by Hoare. We obtain the deformed spin chain model at the fast spin limit for choices of deformed parameters. General ansatz for giant magnons are studied in great detail and complicated dispersion relation is treated perturbatively. We also study several types of hanging string solutions and their charges and spins are analyzed numerically. At last, we explore its pp-wave limit and find its solution only depends on the difference of deformed parameters.
We build the bosonic $η$-deformed $AdS_4\times\mathbb{CP}^3$ background generated by an $r$-matrix that satisfies the modified classical Yang-Baxter equation. In a special limit we find that it is the gravity dual of the noncommutative ABJM theory.
We compute Luscher corrections for a giant magnon in the η-deformed (AdS_5\times S^5)_η using the su(2|2)_q-invariant S-matrix at strong coupling and compare with the finite-size effect of the corresponding string state, derived previously. We find that these two results match and confirm that the su(2|2)_q-invariant S-matrix is describing world-sheet excitations of the η-deformed background.
In this work, we study the effect of $κ$-deformed space on the thermodynamic quantities, this are find through the holographic renormalization that provide the free energy, which is fundamental to derive the another thermodynamic quantities. For this scenario we consider an charged AdS$_{4}$ black hole for an Einstein-Maxwell model where the derivative quadrivector is replaced by a deformed version inspired in Kaniadakis statistics. Besides, we extract the transport coefficient know as electrical conductivity.
We consider a circular string in $\hatγ$ deformed $AdS_5 \times T^{1,1}$ which is localized in the center of $AdS_5$ and winds around the two circles of deformed $T^{1,1}$. We observe chaos in the phase space of the circular string implying non-integrability of string dynamics. The chaotic behaviour in phase space is controlled by energy as well as the deforming parameter $\hatγ$. We further show that the point like object exhibits non-chaotic behaviour. Finally we calculate the Lyapunov exponent for both extended and point like object in support of our first result.
We present the construction of the $λ$-deformation of $AdS_5\times S^5$ superstring from the four dimensional Chern-Simons-type gauge theory. The procedure is applicable to all the semi-symmetric coset models and generalizes the previous construction of $λ$-deformation of the symmetric coset models.
We proceed to study Yang-Baxter deformations of the AdS$_5\times$S$^5$ superstring with the classical Yang-Baxter equation. We make a general argument on the supercoset construction and present the master formula to describe the dilaton in terms of classical $r$-matrices. The supercoset construction is explicitly performed for some classical $r$-matrices and the full backgrounds including the Ramond-Ramond (R-R) sector and dilaton are derived. Within the class of abelian $r$-matrices, the perfect agreement is shown for well-known examples including gravity duals of non-commutative gauge theori…
We investigate the stability of the non-supersymmetric solutions of type-IIB supergravity having an unwarped $AdS$ factor and $λ$-deformed subspaces found in arXiv:1911.12371. Among the plethora of solutions we study the perturbative stability of backgrounds with an $AdS_n$, with $n = 3,4,6$, factor. Our analysis is performed from a lower dimensional effective theory which we construct. We uncover the regions and isolated points in the parameter space of potential perturbative stability.
We find generators of the conformal symmetry for the class of Kerr-Newman-NUT-AdS black holes from the deformed scalar probe equation. We find two classes of solutions for the generators (also known as conformal J and Q pictures). The two classes of deformed generators are the extension of similar generators for the regular conformal symmetry. Moreover, we find that the two pictures can be generalized and extended into a general picture. In each picture, the generators produce an extended local family of SL(2,R)_L \times SL(2,R)_R hidden conformal symmetries for the Kerr-Newman-NUT-AdS black h…
In this paper, we consider a deformed AdS background and study effect of deformation parameter on the pair production rate of the Schwinger effect. The electrostatic potential is important for the pair production in the holographic Schwinger effect. In this paper, we analyze the electrostatic potential in a deformed AdS background and investigate the effect of deformation parameter which may be useful to test of AdS/QCD. In the case of zero temperature we find that larger value of the deformation parameter leads to a smaller value of separation length of the test particles on the probe. Also w…
A family of deformed black branes is employed to examine the confinement/deconfinement phase transition in AdS/QCD. The holographic entanglement entropy (HEE) plays the role of the order parameter driving the confinement/deconfinement phase transition. The binding energy of quark-antiquark bound states and the critical length that makes a null variation of the HEE, together with the critical temperature separating the deconfined quark-gluon plasma to the confined hadronic phase, are discussed in the deformed black brane background, matching current experimental hadronic data.
We study the finite size effect of rigidly rotating and spinning folded strings in $(AdS_3\times S^3)_{\varkappa}$ background. We calculate the leading order exponential corrections to the infinite size dispersion relation of the giant magnon, and single spike solutions. For the spinning folded strings we write the finite size effect in terms of the known Lambert $W$-function.
We investigate Poisson-Lie duals of the $η$-deformed $\mathrm{AdS}_2 \times \mathrm{S}^2 \times \mathrm{T}^6$ superstring. The $η$-deformed background satisfies a generalisation of the type II supergravity equations. We discuss three Poisson-Lie duals, with respect to (i) the full $\mathfrak{psu}(1,1|2)$ superalgebra, (ii) the full bosonic subalgebra and (iii) the Cartan subalgebra, for which the corresponding backgrounds are expected to satisfy the standard type II supergravity equations. The metrics and B-fields for the first two cases are the same and given by an analytic continuation of th…
A family of deformed AdS$_5$-Schwarzschild black branes is here derived, employing the membrane paradigm of AdS/CFT. The solution of the Einstein-Hilbert action, with the Gibbons-Hawking term and a counter-term that eliminates eventual divergences, yields a partition function associated with the dual theory which allows the computation of the entropy, pressure and free energy, as state functions, in the canonical ensemble. AdS/CFT near-horizon methods are then implemented to compute the shear viscosity-to-entropy ratio, then restricting the range of the parameter that defines a family of defor…
The entropic force and the imaginary part of potential experienced by a moving quarkonia in a plasma, are computed in a charged deformed AdS background by holography approaches. In that case, the axis of the moving quarkonia has an arbitrary angle with wind. We show that the charge in deformed AdS background deeply effect on the increasing entropic force and decreasing thermal width. So, the dissociation length of the meson becomes short when charge is increasing. In addition, the entropic force and thermal width are increased by the deformation of the space. Therefore the deformation paramete…
We construct the solution of type IIB supergravity describing the integrable lambda-deformation of the AdS_3 x S^3 supercoset. While the geometry corresponding to the deformation of the bosonic coset has been found in the past, our background is more natural for studying superstrings, and several interesting features distinguish our solution from its bosonic counterpart. We also report progress towards constructing the lambda-deformation of the AdS_5 x S^5 supercoset.
We build string backgrounds for Yang-Baxter deformations of the $AdS_4\times\mathbb{CP}^3$ superstring generated by $r$-matrices satisfying the classical Yang-Baxter equation. We obtain the metric and the NS-NS two-form of the gravity dual corresponding to noncommutative and dipole deformations of ABJM theory, as well as a deformed background with Schrödinger symmetry. The first two backgrounds may also be found by TsT transformations while for the last background we get a new family of non-relativistic ABJM theories with Schrödinger symmetry.
In this work we consider AdS$_3$ gravitational theory with certain mixed boundary conditions at spatial infinity. Using the Chern-Simons formalism of AdS$_3$ gravity, we find that these boundary conditions lead to non-trivial boundary terms, which, in turn, produce exactly the spectrum of the $T\bar{T}/J\bar{T}$-deformed CFTs. We then follow the procedure for constructing asymptotic boundary dynamics of AdS$_3$ to derive the constrained $T\bar{T}$-deformed WZW model from Chern-Simons gravity. The resulting theory turns out to be the $T\bar{T}$-deformed Alekseev-Shatashvili action after disenta…
Integrable boundaries in AdS/CFT: revisiting the Z=0 giant graviton and D7-brane
在AdS/CFT对应中，我们考虑了Z=0巨引力子和Z=0 D 7-膜的世界片边界散射和相应的边界代数.我们考虑两种方法的边界散射，通常由（广义）扭曲的杨氏和q-变形模型的这些边界所管辖的量子仿射余理想子代数。我们表明，q-变形的方法导致边界代数是一个更紧凑的形式比相应的扭曲的杨格，从而有利于使用明确的计算。我们得到的q-变形的反射矩阵的两个边界，在q->1的限制专门使用扭曲的杨格。
We consider the leading finite-size effects on some structure constants for the $η$ - deformed $AdS_5\times S^5$ background in the framework of the semiclassical approach. The leading finite-size corrections are derived for the cases when we have two heavy string states represented by giant magnons and for two different choices of the light states corresponding to dilaton operator with nonzero momentum and primary scalar operators. Since the dual field theory is still unknown, the results obtained here must be considered as conjectures or as predictions from the string theory side.
Beta Function of k Deformed AdS_5 x S^5 String Theory
我们计算了与q=exp（i pi/k）的量子群相关联的k个变形西格玛模型的世界片上可能的边缘耦合的单圈β函数.这包括玻色子主手征模型和对称空间西格玛模型，也包括k变形半对称空间西格玛模型，它描述了AdS_5 x S^5变形的弦。世界片西格玛模型是规范WZW模型对PSU（2，2）超群的电流-电流变形|4）k级。在弦论中，由于PSU（2，2）的Killing形式为零，β函数为零|4）这是另一个证明k变形理论定义了相容的弦论的证据。
In this paper, using the holographic prescription, we study multispin bound states and their dispersion relations over the $ κ$-deformed $ AdS_{3}\times S^{3} $ background. In the first part of our analysis, considering the conformal gauge conditions (associated with the Polyakov action) we explore the dispersion relation associated with spin two bound states at strong coupling. We solve corresponding world-sheet fluctuations and compute all the conserved quantities associated with the stringy dynamics over the deformed background. In the second part of our analysis, we perform similar analysi…
In this paper, considering the correspondence between spin chains and string sigma models, we explore the rotating string solutions over $ η$ deformed $ AdS_5 \times S^{5} $ in the so called fast spinning limit. In our analysis, we focus only on the bosonic part of the full superstring action and compute the relevant limits on both $(R \times S^{3})_η $ and $(R \times S^{5})_η $ models. The resulting system reveals that in the fast spinning limit, the sigma model on $ η$ deformed $S^5$ could be $\textit{approximately}$ thought of as the continuum limit of anisotropic $ SU(3) $ Heisenberg spin …
In this work we study unpolarized spin $1/2$ baryonic deep inelastic scattering (DIS) in the regime of large Bjorken parameter $x$. We calculate the corresponding structure functions $F_{1,2}(x,q^2)$. Our approach is based on an AdS/QCD model with a deformed background, where we consider an exponential factor in the AdS$_5$ metric. Such a deformation implies the introduction of an anomalous dimension in the model. Our results for the structure functions are consistent with those found in the literature from experimental data.
We study the worldsheet scattering theory of the $η$ deformation of the AdS$_\mathsf{5} \times $S$^\mathsf{5}$ superstring corresponding to the purely fermionic Dynkin diagram. This theory is a Weyl-invariant integrable deformation of the AdS$_\mathsf{5} \times $S$^\mathsf{5}$ superstring, with trigonometric quantum-deformed symmetry. We compute the two-body worldsheet S matrix of this string in the light-cone gauge at tree level to quadratic order in fermions. The result factorizes into two elementary blocks, and solves the classical Yang-Baxter equation. We also determine the corresponding e…
Because of the presence of modified warp factors in metric tensors, we use deformed AdS$_5$ spaces to apply the AdS/CFT correspondence to calculate the spectra for even and odd glueballs, scalar and vector mesons, and baryons with different spins. For the glueball cases, we derive their Regge trajectories and compare them with those related to the pomeron and the odderon. For the scalar and vector mesons as well as baryons the determined masses are compatible with the PDG. In particular for these hadrons we found Regge trajectories compatible with another holographic approach as well as with t…
