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 theory will become monopoles in the dual theory, and the monopoles in the original theory will become sources in the dual theory.
In this paper we constructed superloop space duality for a four dimensional supersymmetric Yang-Mills theory with $\mathcal{N} =1$ supersymmetry. This duality reduces to the ordinary loop space duality for the ordinary Yang-Mills theory. It also reduces to the Hodge duality for an abelian gauge theory. Furthermore, the electric charges, which are the sources in the original theory, appear as monopoles in the dual theory. Whereas, the magnetic charges, which appear as monopoles in the original theory, become sources in the dual theory.
In this paper will construct and analyse the superloop space formulation of a $\mathcal{N} =1$ supergauge theory in three dimensions. We will obtain expressions for the connection and the curvature in this superloop space in terms of ordinary supergauge fields. This curvature will vanish, unless there is a monopole in the spacetime. We will also construct a quantity which will give the monopole charge in this formalism. Finally, we will show how these results even hold for a deformed superspace.
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.
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 …
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 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 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 …
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.
An N=1 duality cascade from a deformation of N=4 SUSY Yang-Mills
本文研究了N=1超共形理论的相应形变，它是U（N）N=4超对称Yang-Mills的一个精确的边缘形变.由此产生的理论有一个经典的Higgs分支，它是一个复杂的变形的orbifold C^3/Z_n x Z_n，这是一个非紧的Calabi-Yau空间与孤立的锥状奇点。在模空间中的这些奇点处，理论表现出对偶级联，并流向具有质量间隙的限制理论。通过精确求解相应的全纯矩阵模型，我们计算了对偶级联末端产生的精确量子超势，并精确计算了量子效应如何通过用有限大小的三圈代替锥奇异性来变形经典模空间。局部的结构是变形的锥状，但整体的几何形状是不同的。这种去奇异化的量子形变几何是在对偶级联末端的探测D3-膜的模空间，该对偶级联实现在具有离散挠率的轨道C^3/Z_n x Z_n的形变中的孤立锥状奇点处的（分数）D3-膜的世界体积上。
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.
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 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…
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 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 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…
In flat space, the color/kinematics duality states that perturbative Yang-Mills amplitudes can be written in such a way that kinematic numerators obey the same Jacobi relations as their color factors. This remarkable duality implies BCJ relations for Yang-Mills amplitudes and underlies the double copy to gravitational amplitudes. In this paper, we find analogous relations for Yang-Mills amplitudes in AdS$_4$. In particular we show that the kinematic numerators of 4-point Yang-Mills amplitudes computed via Witten diagrams in momentum space enjoy a generalised gauge symmetry which can be used to…
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 $σ(x)$ …
Gauge-string duality for (non)supersymmetric deformations of N=4 Super Yang-Mills theory
我们考虑AdS/CFT对偶的一个非超对称的例子，它推广了hep-th/0502086中构造的超对称精确边缘变形。我们使用的弦论背景是在hep-th/0503201中通过结合T对偶和角坐标的移动从AdS_5 x S5中找到的。它取决于三个实参数gamma_i，这三个实参数gamma_i决定了变形的5-球面的形状。对偶规范理论具有与N=4 SYM理论相同的场内容，但标量和汤川相互作用被依赖于γ i的相位“变形”。等变形参数gamma_i=gamma的特殊情况对应于N=1的超对称变形。我们将具有三个大角动量的半经典弦的能量与相应规范理论标量算符的1圈反常维数进行了比较，发现它们与标准AdS/CFT对偶的SU（3）扇区中的情况相匹配。在gamma_i相等的超对称情况下，这将我们以前的工作（hep-th/0503192）的结果从2自旋扇区扩展到3自旋扇区。这个扩展证明是相当不平凡的。为了使相应的低能有效"Landau-Lifshitz“作用量在弦论和规范理论侧相匹配，一种方法是对代表单圈规范理论伸缩算符的自旋链哈密顿量进行特殊选择。这种选择适用于低能近似，即它允许在连续相干态有效作用下捕获正确的真空态和自旋链的宏观自旋波扇区。
We study presence of an additional symmetry of a generic central potential in the $κ$-space-time. An explicit construction of Fradkin and Bacry, Ruegg, Souriau (FBRS) for a central potential is carried out and the piece-wise conserved nature of the vector is established. We also extend the study to Kepler systems with a drag term, particularly Gorringe-Leach equation is generalized to the $κ$-deformed space. The possibility of mapping Gorringe-Leach equation to an equation with out drag term is exploited in associating a similar conserved vector to system with a drag term. An extension of dual…
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.
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…
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 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.
