Using a Lorentz invariant deformed string/gauge duality model at finite temperature we calculate the thermal fluctuation and the corresponding linear response, verifying the fluctuation-dissipation theorem. The deformed AdS$_5$ is constructed by the insertion of an exponential factor $\exp(k/r^2)$ in the metric. We also compute the string energy and the mean square displacement in order to investigate the ballistic and diffusive regimes. Furthermore we have studied the dissipation and the linear response in the zero temperature scenario.
In this work, we study the electric and magnetic Sachs form factors for proton and neutron by using a deformed gravity/gauge model. We describe holographically baryons as well as gauge bosons which are ruled by the parameters $k_{B}$ and $k_γ$, associated with confinement and kinematical energy scales, respectively. Then, we construct the interaction action and calculate the electric and magnetic form factors for the proton and the neutron, and their electromagnetic sizes. The obtained results are compatible with those found in the literature from experimental and theoretical data.
In this work we study the fluctuation and dissipation of a string attached to a brane in a deformed and backreated AdS-Schwarzschild spacetime. This space is a solution of Einstein-dilaton equations and contains a conformal exponential factor $\exp(k/r^2)$ in the metric. We consider the backreaction contributions coming only from the exponential warp factor on the AdS-Schwarzschild black hole, where the string and brane are in the probe approximation. Within this Lorentz invariant holographic model we have computed the admittance, the diffusion coefficient, the two-point functions and the regu…
A modification of the standard product used in local field theory by means of an associative deformed product is proposed. We present a class of deformed products, one for every spin S=0,1/2,1, that induces a nonlocal theory, displaying different form for different fields. This type of deformed product is naturally supersymmetric and it has an intriguing duality.
The $1/x^{2}$ deformed $c=1$ matrix model is studied at finite radius and non-zero cosmological constant. Calculational techniques are presented and illustrated in some examples. Furthermore, a new kind of $R \rightarrow 1/R$ duality is discovered which mixes different genus.
In this paper, we will analyse the superloop space formalism for a four dimensional supersymmetric Yang-Mills theory in deformed superspace. We will deform the $\mathcal{N} =1$ superspace by imposing non-anticommutativity. This non-anticommutative deformation of the superspace will break half the supersymmetry of the original theory. So, this theory will have $\mathcal{N} =1/2$ supersymmetry. We will analyse the superloop space duality for this deformed supersymmetric Yang-Mills theory using the $\mathcal{N} =1/2$ superspace formalism. We will demonstrate that the sources in the original theor…
In this paper, we analyze the modification of integrable models in the $κ$-deformed space-time. We show that two dimensional isotropic oscillator problem, Kepler problem and MICZ-Kepler problem in $κ$-deformed space-time admit integrals of motion as in the commutative space. We also show that the duality equivalence between $κ$-deformed Kepler problem and $κ$-deformed two-dimensional isotropic oscillator explicitly, by deriving Bohlin-Sundman transformation which maps these two systems. These results are valid to all orders the the deformation parameter.
An attempt is made to formulate Gaiotto's S-duality relations in an explicit quantitative form. Formally the problem is that of evaluation of the Racah coefficients for the Virasoro algebra, and we approach it with the help of the matrix model representation of the AGT-related conformal blocks and Nekrasov functions. In the Seiberg-Witten limit, this S-duality reduces to the Legendre transformation. In the simplest case, its lifting to the level of Nekrasov functions is just the Fourier transform, while corrections are related to the beta-deformation. We calculate them with the help of the mat…
We study the $SU(2)_k/U(1)$-parafermion model perturbed by its first thermal operator. By formulating the theory in terms of a (perturbed) fermionic coset model we show that the model is equivalent to interacting WZW fields modulo free fields. In this scheme, the order and disorder operators of the $Z_k$ parafermion theory are constructed as gauge invariant composites. We find that the theory presents a duality symmetry that interchanges the roles of the spin and dual spin operators. For two particular values of the coupling constant we find that the theory recovers conformal invariance and th…
In ${\cal N}=5, 6, 8$ supergravities there are hidden symmetries of equations of motion, described by duality groups $SU(1,5), \, SO^*(12), \, E_{7(7)}$ respectively. UV divergences and known candidate counterterms violate the deformed duality symmetry current conservation. Extra higher derivative terms in the action are required to restore duality. We study the effect of a two-vector part of the counterterm for ${\cal N}\geq 5$ supergravities using the universality of the symplectic structure of extended supergravities. We construct a compact form of a deformed action with infinite number of …
We enhance the action of higher abelian gauge theory associated to a gerbe on an M5-brane with an action of a torus ${\mathbb T}^n (n\ge 2)$, by a noncommutative ${\mathbb T}^n$-deformation of the M5-brane. The ingredients of the noncommutative action and equations of motion include the deformed Hodge duality, deformed wedge product, and the noncommutative integral over the noncommutative space obtained by strict deformation quantization. As an application we then introduce a variant model with an enhanced action in which we show that the corresponding partition function is a modular form, whi…
We study the non-perturbative properties of N=2 super conformal field theories in four dimensions using localization techniques. In particular we consider SU(2) gauge theories, deformed by a generic epsilon-background, with four fundamental flavors or with one adjoint hypermultiplet. In both cases we explicitly compute the first few instanton corrections to the partition function and the prepotential using Nekrasov's approach. These results allow to reconstruct exact expressions involving quasi-modular functions of the bare gauge coupling constant and to show that the prepotential terms satisf…
In this work we study fluctuations and dissipation of a string in a deformed anti-de Sitter (AdS) space at finite temperature and density. The deformed AdS space is a charged black hole solution of the Einstein-Maxwell-Dilaton action. In this background we take into account the backreaction on the horizon function from an exponential deformation of the AdS space. From this model we compute the admittance and study the influence of the temperature and the chemical potential on it. We calculate the two-point correlations functions, and the mean square displacement for bosonic and fermionic cases…
The so-called homogeneous Yang-Baxter (YB) deformations can be considered a non-abelian generalization of T-duality--shift--T-duality (TsT) transformations. TsT transformations are known to preserve conformal symmetry to all orders in $α'$. Here we argue that (unimodular) YB deformations of a bosonic string also preserve conformal symmetry, at least to two-loop order. We do this by showing that, starting from a background with no NSNS-flux, the deformed background solves the $α'$-corrected supergravity equations to second order in the deformation parameter. At the same time we determine the re…
We consider various integrable two-parameter deformations of the $AdS_3 \times S^3 \times T^4$ superstring with quantum group symmetry. Working on the string worldsheet in light-cone gauge and to quadratic order in fermions, we obtain their common massive tree-level two-body S matrix, which matches the expansion of the conjectured exact $q$-deformed S matrix. We then analyze the behavior of the exact S matrix under mirror transformation -- a double Wick rotation on the worldsheet -- and find that it satisfies a mirror duality relation analogous to the distinguished $q$-deformed $AdS_5 \times S…
We present general formulae for the TsT transformation (T-duality, shift, T-duality) of type II string backgrounds and open string boundary conditions. The TsT transformation provides a systematic procedure to find string theory duals of gauge theories with deformed products of fields in the lagrangian, and the duals can be analyzed by using transformed D-brane probes. As examples illustrating some features of the deformed theories, we consider the known backgrounds dual to non-commutative, dipole and beta-deformed N=4 Super Yang-Mills as well as new backgrounds dual to deformations of the rec…
The auxiliary-deformed Breitenlohner-Maison model: duality frames and higher-dimensional origin
Asia Pacific Center for Theoretical Physics (APCTP), Postech（亚太理论物理中心（APCTP），浦项科技大学）；High Energy Physics Research Unit, Faculty of Science Chulalongkorn University（朱拉隆功大学理学院高能物理研究单元）；Max-Planck-Institut für Gravitationsphysik (Albert-Einstein-Institut)（马克斯·普朗克引力物理研究所（爱因斯坦研究所））
We first perform bosonic T-duality transformation on one of the marginal TsT (T-duality, shift, T-duality)-deformed $AdS_5\times S_5$ spacetime, which corresponds to 4D $\mathcal{N}=4$ non-commutative super Yang-Mills theory (NCSYM). We then construct the solution to killing spinor equations of the resulting background, and perform the fermionic T-duality transformation. The final dual geometry becomes the usual $AdS_5\times S_5$ but with the constant NS-NS B-field depending on the non-commutative parameter. As applications, we study the gluon scattering amplitude and open string (Wilson loop)…
We derive the q-deformation of the chiral Gross-Taylor holomorphic string large N expansion of two dimensional SU(N) Yang-Mills theory. Delta functions on symmetric group algebras are replaced by the corresponding objects (canonical trace functions) for Hecke algebras. The role of the Schur-Weyl duality between unitary groups and symmetric groups is now played by q-deformed Schur-Weyl duality of quantum groups. The appearance of Euler characters of configuration spaces of Riemann surfaces in the expansion persists. We discuss the geometrical meaning of these formulae.
We investigate epsilon-deformed N=2 superconformal gauge theories in four dimensions, focusing on the N=2* and Nf=4 SU(2) cases. We show how the modular anomaly equation obeyed by the deformed prepotential can be efficiently used to derive its non-perturbative expression starting from the perturbative one. We also show that the modular anomaly equation implies that S-duality is implemented by means of an exact Fourier transform even for arbitrary values of the deformation parameters, and then we argue that it is possible, perturbatively in the deformation, to choose appropriate variables such …
We implement the momentum dissipation introduced by spatial linear axionic fields in a holographic model without self-duality, broke by Weyl tensor coupling to Maxwell field, and study its response. It is found that for the positive Weyl coupling parameter $γ>0$, the momentum dissipation characterized by parameter $\hatα$ drives the boundary conformal field theory (CFT), in which the conductivity exhibits a peak at low frequency, into the incoherent metallic phase with a dip, which is away from CFT due to the introduction of axionic fields. While for $γ<0$, an oppositive scenario is found. Our…
From a deformed AdS$_5$ space, we used the string/gauge duality to study the deep inelastic scattering for unpolarized fermions with spin 1/2, considering the large Bjorken $x$ parameter regime. Here, we also took into account an anomalous dimension of an operator which represents fermions at the boundary. From this analysis, we compute the corresponding structure functions, which are dependent on $x$ and on the photon virtuality $q$. The results achieved are in agreement with the experimental data.
We study five dimensional AGT correspondence by means of the q-deformed beta-ensemble technique. We provide a special basis of states in the q-deformed CFT Hilbert space consisting of generalized Macdonald polynomials, derive the loop equations for the beta-ensemble and obtain the factorization formulas for the corresponding matrix elements. We prove the spectral duality for Nekrasov functions and discuss its meaning for conformal blocks. We also clarify the relation between topological strings and q-Liouville vertex operators.
Inspired by a recently proposed Duality and Conformal invariant modification of Maxwell theory (ModMax), we construct a one-parameter family of two-dimensional dynamical system in classical mechanics that share many features with the ModMax theory. It consists of a couple of $\sqrt{T\bar{T}}$-deformed oscillators that nevertheless preserves duality $(q \rightarrow p,p \rightarrow -q)$ and depends on a continuous parameter $γ$, as in the ModMax case. Despite its non-linear features, the system is integrable. Remarkably can be interpreted as a pair of two coupled oscillators whose frequencies de…
The basic cosmological distances are linked by the Etherington cosmic distance duality relation, $η(z) = D_{L}(z)(1+z)^{-2}/D_{A}(z) \equiv 1$, where $D_{L}$ and $D_{A}$ are, respectively, the luminosity and angular diameter distances. In order to test its validity, some authors have proposed phenomenological expressions for $η(z)$ thereby deforming the original Etherington's relation and comparing the resulting expressions with the available and future cosmological data. The relevance of such studies is unquestionable since any violation of the cosmic distance duality relation could be the si…
We show that the geometric interpretation of D-branes in WZW models as twisted conjugacy classes persists in the $λ$--deformed theory. We obtain such configurations by demanding that a monodromy matrix constructed from the Lax connection of the $λ$--deformed theory continues to produce conserved charges in the presence of boundaries. In this way the D-brane configurations obtained correspond to `integrable' boundary configurations. We illustrate this with examples based on $SU(2)$ and $SL(2,\mathbb{R})$, and comment on the relation of these D-branes to both non-Abelian T-duality and Poisson-Li…
We study the Klein four-group $(K_4)$ symmetry of the time-dependent Schrödinger equation for the conformal mechanics model of de Alfaro-Fubini-Furlan (AFF) with confining harmonic potential and coupling constant $g=ν(ν+1)\geq -1/4$. We show that it undergoes a complete or partial (at half-integer $ν$) breaking on eigenstates of the system, and is the automorphism of the $\mathfrak{osp}(2,2)$ superconformal symmetry in super-extensions of the model by inducing a transformation between the exact and spontaneously broken phases of $\mathcal{N}=2$ Poincaré supersymmetry. We exploit the $K_4$ symm…
A covariantly constant dynamical two-form is exploited on a $D_3$-brane to obtain its gravity dual action, governing an $S^3$ deformed $AdS_5$ black hole, in a type IIB string theory on $S^1\times K3$. We invoke the Kaluza-Klein compactification to work out the open/closed string duality. Interestingly, the Reissner-Nordstrom black hole is obtained on the "non-Reimannian" braneworld.
In this note, we study different limits of an Omega-deformed (2,0) six-dimensional gauge theory realized in a M-theory fluxtrap background. Via a chain of dualities, we connect the Omega-deformed SYM to a new four-dimensional gauge theory which we refer to as the reciprocal gauge theory. This theory has several properties in common with Liouville field theory, such as its gauge coupling b^2 =ε_2 / ε_1, and its behavior under S-duality. Finally, we realize the BPS states on the SYM side of the AGT correspondence and follow them along the chain of dualities. In the fluxtrap frame, we are dealing…
A weak quantum mechanical coupling is constructed permitting superluminal communication within a preferred region of a gravitating AdS_5 spacetime. This is achieved by adding a spatially non-local perturbation of a special kind to the Hamiltonian of a four-dimensional conformal field theory with a weakly-coupled AdS dual, such as maximally supersymmetric Yang-Mills theory. In particular, two issues are given careful treatment: (1) the UV-completeness of our deformed CFT, guaranteeing the existence of a ``deformed string theory'' AdS dual, and (2) the demonstration that superluminal effects can…
The thermal deformation of the critical point action of the 2D tricritical Ising model gives rise to an exact scattering theory with seven massive excitations based on the exceptional $E_7$ Lie algebra. The high and low temperature phases of this model are related by duality. This duality guarantees that the leading and sub-leading magnetisation operators, $σ(x)$ and $σ'(x)$, in either phase are accompanied by associated disorder operators, $μ(x)$ and $μ'(x)$. Working specifically in the high temperature phase, we write down the sets of bootstrap equations for these four operators. For $σ(x)$ …
Deformed Schur Indices of BCD-type for N=4 Super Yang-Mills and Symmetric Functions
Interdisciplinary Center for Theoretical Study, University of Science and Technology of China（中国科学技术大学理论物理交叉中心）；Peng Huanwu Center for Fundamental Theory（彭桓武理论物理中心）
In this paper we study string theory in the background $\mathcal{M}_3$ that interpolates between $AdS_3$ in the IR and linear dilaton spacetime $\mathbb{R}^{1,1}\times\mathbb{R}_ϕ$ in the UV. Via holographic duality this background corresponds to $\rm{CFT}_2$ deformed by a dimension $(2,2)$ operator. Here we discuss the holographic Wilson loop in such a model and shed more light in support of the non-local structure of the theory (Little String Theory (LST)) in the UV. We also discuss quantum and thermal phase transitions of the boundary theory.
We reconsider topological string realization of SU(N) Chern-Simons theory on S^3. At large N, for every knot K in S^3, we obtain a polynomial A_K(x,p;Q) in two variables x,p depending on the t'Hooft coupling parameter Q=e^{Ng_s}. Its vanishing locus is the quantum corrected moduli space of a special Lagrangian brane L_K, associated to K, probing the large N dual geometry, the resolved conifold. Using a generalized SYZ conjecture this leads to the statement that for every such Lagrangian brane L_K we get a distinct mirror of the resolved conifold given by uv=A_K(x,p;Q). Perturbative corrections…
We study supersymmetric Sp(2N) gauge theories with matter in the antisymmetric tensor representation and F fundamentals. For F=6 we solve the theory exactly in terms of confined degrees of freedom and a superpotential. By adding mass terms we obtain the theories with F<6 which we find to exhibit a host of interesting non-perturbative phenomena: quantum deformed moduli spaces with N constraints, instanton-induced superpotentials and non-equivalent disjoint branches of moduli spaces. We find a simple dual for F=8 and no superpotential. We show how the F=4 and F=2 theories can be modified to brea…
We establish that the unusual two-form gauge transformations needed in the Green-Schwarz anomaly cancellation mechanism fit naturally into an $α'$-deformed generalized geometry. The algebra of gauge transformations is a consistent deformation of the Courant bracket and features a nontrivial modification of the diffeomorphism group. This extension of generalized geometry emerged from a `doubled $α'$-geometry', which provides a construction of exactly gauge and T-duality invariant $α'$ corrections to the effective action.
We investigate color-kinematics duality for gauge-theory amplitudes produced by the pure nonabelian Yang-Mills action deformed by higher-dimension operators. For the operator denoted by F^3, the product of three field strengths, the existence of color-kinematic dual representations follows from string-theory monodromy relations. We provide explicit dual representations, and show how the double-copy construction of gravity amplitudes based on them is consistent with the Kawai-Lewellen-Tye relations. It leads to the amplitudes produced by Einstein gravity coupled to a dilaton field phi, and defo…
In this paper we have analyzed the $κ$-deformed Minkowski spacetime through the light of the interference phenomena in QFT where two opposite chiral fields are put together in the same multiplet and its consequences are discussed. The chiral models analyzed here are the chiral Schwinger model, its generalized version and its gauge invariant version, where a Wess-Zumino term were added. We will see that the final actions obtained here are in fact related to the original ones via duality transformations.
We use localization techniques to study several duality proposals for supersymmetric gauge theories in three dimensions reminiscent of Seiberg duality. We compare the partition functions of dual theories deformed by real mass terms and FI parameters. We find that Seiberg-like duality for N=3 Chern-Simons gauge theories proposed by Giveon and Kutasov holds on the level of partition functions and is closely related to level-rank duality in pure Chern-Simons theory. We also clarify the relationship between the Giveon-Kutasov duality and a duality in theories of fractional M2 branes and propose a …
In this Letter, based on the notion of gauge/gravity duality, we compute $ q $ SYK spectra in the presence of Yang-Baxter (YB) deformations. The gravitational counterpart of this duality turns out to be the YB deformed Almheiri-Polchinski (AP) model embodied with hyperbolic potential for the dilaton. Following Kaluza-Klein reduction on $ (AdS_2)_η\times (S^1/ Z_2) $, we compute the deformed Green's function that reproduces the original $ q $ SYK spectrum in the limit of vanishing deformations.
These lectures trace the origin of string theory as a theory of hadronic interactions (predating QCD itself) to the present ideas on how the QCD string may arise in Superstring theory in a suitably deformed background metric. The contributions of 'tHooft's large Nc limit, Maldacena's String/Gauge duality conjecture and lattice spectral data are emphasized to motivate and hopefully guide further efforts to define a fundamental QCD string.
We construct the low-energy effective field theory for a D3-brane in constant R-R 2-form potential background as the S-dual theory of a D3-brane in NS-NS B-field background. Despite the non-Abelian algebra of the noncommutative U(1) gauge symmetry, the electromagnetic duality transformation can be carried out to all orders, and the dual Lagrangian is given in a compact form. The gauge algebra is found to be a mixture of a deformed area-preserving diffeomorphism and the usual U(1) gauge symmetry.
The purpose of this work is two fold. Working in the framework of $(1+1)D$ Lorentz violating field theories we will investigate in the first place the general claim that fermionic interactions may be equivalent to a deformation of the canonical structure of the theory. Second the deformed theory will be studied using duality reasoning to address the behavior of the Infra-Red and Ultra-Violet regimes.
We consider the correspondence between the spinning string solutions in Lunin-Maldacena background and the single trace operators in the Leigh-Strassler deformation of N=4 SYM. By imposing an appropriate rotating string ansätz on the Landau-Lifshitz reduced sigma model in the deformed SU(2) sector, we find two types of `elliptic' solutions with two spins, which turn out to be the solutions associated with the Neumann-Rosochatius system. We then calculate the string energies as functions of spins, and obtain their explicit forms in terms of a set of moduli parameters. On the deformed spin-chain…
We derive the Maxwell's equations on the $κ$-deformed spacetime, valid up to first order in the deformation parameter, using the Feynman's approach. We show that the electric-magnetic duality is a symmetry of these equations. It is also shown that the laws of electrodynamics are {\it different} for particles of equal charges, but with different masses. We show that the Poincare angular momentum, required to maintain the usual Lorentz algebra structure, do not get any $κ$-dependent corrections.
In this Letter, based on the notion of Gauge/Gravity duality we explore the low frequency behaviour associated with the retarded two point correlators in the ground state of the strongly correlated quantum liquid that is dual to $ η$- deformed background in ($ 2+1 $)D. The massless charge carriers in the dual gauge theory are sourced due to some \textit{probe} $ N_f $ flavour $ Dp $ brane configurations in the bulk. In our analysis we stick to the NS sector and compute the two point correlators by turning on fluctuations associated with the worldvolume gauge fields in the bulk spacetime. Our a…
We investigate $α'$ corrections of bosonic strings in the framework of double field theory. The previously introduced "doubled $α'$-geometry" gives $α'$-deformed gauge transformations arising in the Green-Schwarz anomaly cancellation mechanism but does not apply to bosonic strings. These require a different deformation of the duality-covariantized Courant bracket which governs the gauge structure. This is revealed by examining the $α'$ corrections in the gauge algebra of closed string field theory. We construct a four-derivative cubic double field theory action invariant under the deformed gau…
The partition functions of refined topological strings(A-models) are computed, which give rise to the circle-compactified five-dimensional supersymmetric linear quiver gauge theories in generic (not necessarily self-dual) Omega backgrounds. Based on the slicing independence conjecture of refined topological string partition functions, it is demonstrated explicitly that the duality exists between $SU(N)^{M-1}$ and $SU(M)^{N-1}$ supersymmetric linear quiver gauge theories, even in generic Omega backgrounds. It is found that the relations between string moduli and gauge moduli are deformed from t…
We compute some normalized structure constants in the $η$-deformed $AdS_5\times S^5$ in the framework of the semiclassical approach. This is done for the cases when the "heavy" string states are finite-size giant magnons carrying one angular momentum and for three different choices of the "light" state: primary scalar operators, dilaton operator with nonzero momentum, singlet scalar operators on higher string levels. 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. Keywords: Gauge/string dua…
We establish duality between real forms of the quantum deformation of the 4-dimensional orthogonal group studied by Fioresi et al. and the classification work made by Borowiec et al.. Classically these real forms are the isometry groups of $\mathbb{R}^4$ equipped with Euclidean, Kleinian or Lorentzian metric. A general deformation, named $q$-linked, of each of these spaces is then constructed, together with the coaction of the corresponding isometry group.
We study large N dualities for a class of ${\cal N} = 1$ theories realized on type IIB D5 branes wrapping 2-cycles of local Calabi-Yau threefolds which is obtained from resolving orbifolded conifolds or as effective field theories on D4 branes in type IIA brane configurations. The field theory is $\mathcal{N} =1$ supersymmetric $\prod U(N_{ij})$ Yang-Mills gauge theory. Strong coupling effects are analyzed in the deformed geometry. We propose open-closed string duality via a geometric transition in toric geometry. The T-dual type IIA picture and M-theory lifting are also considered.
We study the soft breaking of N=2 self-dual gauge theories down to N=0 by promoting the coupling constant and hypermultiplet masses to spurions, and we analyze the microscopic duality symmetry in the resulting models. Explicit formulae are given for the Seiberg-Witten periods and couplings in the case of SU(2), and we perform a numerical study of the non-supersymmetric vacuum structure in the case of the mass-deformed N=4 SU(2) gauge theory. Although the softly broken model has a well-defined behavior under the duality symmetry, the stable vacua are in a confining phase. We also extend some of…
