BMS symmetry, which is the asymptotic symmetry at null infinity of flat spacetime, is an important input for flat holography. In this paper, we give a holographic calculation of entanglement entropy and Rényi entropy in three dimensional Einstein gravity and Topologically Massive Gravity. The geometric picture for the entanglement entropy is the length of a spacelike geodesic which is connected to the interval at null infinity by two null geodesics. The spacelike geodesic is the fixed points of replica symmetry, and the null geodesics are along the modular flow. Our strategy is to first reformulate the Rindler method for calculating entanglement entropy in a general setup, and apply it for BMS invariant field theories, and finally extend the calculation to the bulk.
In monolayer transition metal dichalcogenides (TMDs), electrons in opposite K valleys are subject to opposite effective Zeeman fields, which are referred to as Ising spin-orbit coupling (SOC) fields. The Ising SOC, originated from in-plane mirror symmetry breaking, pins the electron spins to the out-of-plane directions, and results in the newly discovered Ising superconducting states with strongly enhanced upper critical fields. In this work, we show that the Ising SOC generates equalspin triplet Cooper pairs with spin polarized in the in-plane directions. Importantly, the spin-triplet Cooper pairs can induce superconducting pairings in a half-metal wire placed on top of the TMD and result in a topological superconductor with Majorana end states. Direct ways to detect equal-spin triplet Cooper pairs and the differences between Ising superconductors and Rashba superconductors are discussed.
We study several aspects of holographic entanglement in two models known as flat 3 /BMSFT and (W)AdS 3 /WCFT. These are two examples of holography beyond AdS/CFT where the boundary field theories are not Lorentz invariant but still feature an infinite set of local symmetries. In the first example, BMS-invariant field theories (BMSFTs) are conjectured to provide a holographic description of quantum gravity in asymptotically flat three-dimensional spacetimes; while in the second example, warped conformal field theories (WCFTs) are proposed to describe quantum gravity in warped AdS 3 or AdS 3 backgrounds with Dirichlet-Neumann boundary conditions. In particular, we derive the modular Hamiltonian for single intervals in both BMSFTs and WCFTs and find the holographic duals in the bulk using the covariant formulation of gravitational charges. We also extend the first law of entanglement entropy to these models of non-AdS holography and discuss the bound on "modular chaos" introduced recently in the context of the AdS/CFT correspondence.
We investigate the behaviour of two-dimensional quantum field theories with N = (0, 2) supersymmetry under a deformation induced by the "TT " composite operator. We show that the deforming operator can be defined by a point-splitting regularisation in such a way as to preserve N = (0, 2) supersymmetry. As an example of this construction, we work out the deformation of a free N = (0, 2) theory, compare to that induced by the Noether stress-energy tensor and argue that, despite their apparent difference, they are equivalent on-shell. Finally, we show that the N = (0, 2) supersymmetric deformed action actually possesses N = (2, 2) symmetry, half of which is non-linearly realised. arXiv:1904.04760v3 [hep-th]
We propose a holographic entanglement entropy prescription for general states and regions in two models of holography beyond AdS/CFT known as flat3/BMSFT and (W)AdS3/WCFT. Flat3/BMSFT is a candidate of holography for asymptotically flat three- dimensional spacetimes, while (W)AdS3/WCFT is relevant in the study of black holes in the real world. In particular, the boundary theories are examples of quantum field theories that feature an infinite dimensional symmetry group but break Lorentz invariance. Our holographic entanglement entropy proposal is given by the area of a swing surface that consists of ropes, which are null geodesics emanating from the entangling surface at the boundary, and a bench, which is a spacelike geodesic connecting the ropes. The proposal is supported by an extension of the Lewkowycz-Maldacena argument, reproduces previous results based on the Rindler method, and satisfies the first law of entanglement entropy.
The TT deformation of a supersymmetric two-dimensional theory preserves the original supersymmetry. Moreover, in several interesting cases the deformed theory possesses additional non-linearly realized supersymmetries. We show this for certain N = (2, 2) models in two dimensions, where we observe an intriguing similarity with known N = 1 models in four dimensions. This suggests that higher-dimensional models with non-linearly realized supersymmetries might also be obtained from TT -like flow equations.We show that in four dimensions this is indeed the case for N = 1 Born-Infeld theory, as well as for the Goldstino action for spontaneously broken N = 1 supersymmetry. arXiv:1910.01599v1 [hep-th] 3 Oct 2019Contents 1 Introduction 1 2 D = 2 N = (2, 2) Flows and Non-Linear N = (2, 2) Supersymmetry 4 2.1 TT deformations with N = (2, 2) supersymmetry 4 2.2 The TT -deformed twisted-chiral model and partial-breaking 7 2.3 The TT -deformed chiral model and partial-breaking 13 3 D = 4 T 2 Deformations and Their Supersymmetric Extensions 16 3.1 Comments on the T 2 operator in D = 4 16 3.2 D = 4 N = 1 supercurrent-squared operator 18 4 Bosonic Born-Infeld As a T 2 Flow 20 5 Supersymmetric Born-Infeld From Supercurrent-Squared Deformation 22 7 Conclusions and Outlook 33 A Deriving a Useful On-shell Identity 36 construct two models describing the partial supersymmetry breaking pattern N = (4, 4) → N = (2, 2) in D = 2. These models have manifest N = (2, 2) supersymmetry from the superspace structure used in their construction, but they also admit another hidden nonlinear N = (2, 2) supersymmetry. It turns out the resulting actions are exactly the same as the N = (2, 2) chiral and twisted chiral TT -deformed actions of [18]. The intriguing relation between non-linear supersymmetry and TT therefore persists for models with manifest N = (2, 2) supersymmetry. Interestingly, even the D = 2 Volkov-Akulov action, describing the dynamics of the Goldstinos which arise from the spontaneous breaking of N = (2, 2) supersymmetry, satisfies a TT flow equation [21]. This collection of examples motivates us to see whether any higher-dimensional theories with non-linear supersymmetries might also satisfy TT -like flow equations. It has been known for more than two decades that the Bagger-Galperin action for the D = 4 N = 1 Born-Infeld theory describes N = 2 → N = 1 partial supersymmetry breaking [22]. Does the Bagger-Galperin action arise from a TT -like deformation of N = 1 Maxwell theory? That the linear order deformation is given by a supercurrent-squared operator was noted long ago in [23]. Much more recently, bosonic Born-Infeld theory was shown to satisfy a T 2 flow equation, where T 2 is an operator quadratic in the stress-energy tensor [24]. In this work, we explicitly show that the Bagger-Galperin action indeed satisfies a supercurrentsquared flow equation, generalizing the observation of [23] to all orders in the deformation parameter. The supercurrent-squared deformation operator is constructed from supercurrent multiplets, but its to...
Celestial holography promisingly reformulates the scattering amplitude holographically in terms of celestial conformal field theory living at null infinity. Recently, an infinite-dimensional symmetry algebra was discovered in Einstein-Yang-Mills theory. The starting point in the derivation is the celestial OPE of two soft currents, and the key ingredient is the summation of $$ \overline{\mathrm{SL}\left(2,\mathbb{R}\right)} $$ SL 2 ℝ ¯ descendants in OPE. In this paper, we consider the supersymmetric Einstein-Yang-Mills theory and obtain the supersymmetric extension of the holographic symmetry algebra. Furthermore, we derive infinitely many Ward identities associated with the infinite soft currents which generate the holographic symmetry algebra. This is realized by considering the OPE between a soft symmetry current and a hard operator, and then summing over its $$ \overline{\mathrm{SL}\left(2,\mathbb{R}\right)} $$ SL 2 ℝ ¯ descendants. These Ward identities reproduce the known Ward identities corresponding to the leading, sub-leading, and sub-sub-leading soft graviton theorems as well as the leading and sub-leading soft gluon theorems. By performing shadow transformations, we also obtain infinitely many shadow Ward identities, including the stress tensor Ward identities for sub-leading soft graviton. Finally, we use our procedure to discuss the corrections to Ward identities in effective field theory (EFT), and reproduce the corrections to soft theorems at sub-sub-leading order for graviton and sub-leading order for photon. For this aim, we derive general formulae for the celestial OPE and its corresponding Ward identities arising from a cubic interaction of three spinning massless particles. Our formalism thus provides a unified framework for understanding the Ward identities in celestial conformal field theory, or equivalently the soft theorems in scattering amplitude.
We study the general deformation of N = 2 supersymmetry transformations of a vector multiplet that forms a (constant) triplet under the SU (2) R-symmetry corresponding to the magnetic dual of the triplet of the Fayet-Iliopoulos (FI) parameters. We show that in the presence of both triplets, the induced scalar potential of a vector multiplet with generic prepotential has always a minimum that realises partial breaking of N = 2 → N = 1 supersymmetry. We then consider the impact of the deformation in the Dirac-Born-Infeld (DBI) action where one supersymmetry is non-linearly realised, described by a nilpotent constraint on the deformed N = 2 chiral-chiral superfield. We show that the generic magnetic deformation induces an ordinary FI D-term along the linear supersymmetry via the theta-angle. Moreover, we argue that the resulting action differs on-shell from the standard one (DBI+FI) by fermionic contributions.
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