We assess the role of a resonant spectrum in the AdS instability, and quantify the extent to which breaking the resonant spectrum of AdS can restore stability. Specifically, we study non-collapsing `multi-oscillator' solutions in AdS under various boundary conditions that allow for both resonant and non-resonant spectra. We find non-collapsing two mode, equal amplitude solutions in the non-resonant Robin case, and that these solutions vanish in the fully resonant Dirichlet case. This is consistent with non-resonant stability, and with the idea that stable solutions in the Dirichlet case are all single-mode dominated. Surprisingly, when the boundary condition is Neumann, we find non-collapsing solutions arbitrarily close to AdS that are not single-mode dominated, despite the spectrum being fully resonant.
Considering a doubly holographic model, we study the evolution of holographic subregion complexity corresponding to deformations of bath state by a relevant scalar operator, which corresponds to a renormalization group flow from the AdS-Schwarzschild to the Kasner universe in the bulk. The subregion complexity shows a discontinuous jump at Page time at a fixed perturbation, where the discontinuity depends solely on the system's parameters. We show that the amount of discontinuity decreases with the perturbation as well as with the scaling dimension of the relevant scalar operator.
The method of minimal geometric deformation (MGD) is used to derive static, strongly gravitating, spherically symmetric, compact stellar distributions. The trace and Weyl anomalies are then employed to probe the MGD in the holographic setup, as a realistic model, playing a prominent role in AdS/CFT.
In this paper, we study the bulk entanglement entropy evolution in conical BTZ black bole background using the heat kernel method. This is motivated by exploring the new examples where quantum corrections of entanglement entropy give the leading contribution. We find that in the large black hole limit the bulk entanglement entropy decreases under the double-trace deformation which is consistent with the holographic $c$ theorem and in the small black hole limit the bulk entanglement entropy increases under the double-trace deformation.
String theory on AdS$_3$ with NS-NS fluxes admits a solvable irrelevant deformation which is close to the $T\bar{T}$ deformation of the dual CFT$_2$. This consists of deforming the worldsheet action, namely the action of the $SL(2,\mathbb{R})$ WZW model, by adding to it the operator $J^-\bar{J}^-$, constructed with two Kac-Moody currents. The geometrical interpretation of the resulting theory is that of strings on a conformally flat background that interpolates between AdS$_3$ in the IR and a flat linear dilaton spacetime with Hagedorn spectrum in the UV, having passed through a transition reg…
We extend the analysis of boundedness and stability, initiated for scalar fields in anti de Sitter space in a previous work, to the case of vector fields. We show that the double trace deformation of Marolf and Ross is distinct from the double trace deformation of Witten. The former gives rise to an $SL(2,{\bf R})$ family of theories whereas the latter gives rise to an independent $SL(2,{\bf Z})$. We analyze the finite temperature two-point correlation function of current operators and infer the susceptibility and spectrum of low lying states. We discuss various physical features exhibited by …
We compute the bulk entanglement entropy of a massive scalar field in a Poincare AdS with the Dirichlet and Neumann boundary condition when we trace out a half space. Moreover, by taking into account the quantum back reaction to the minimal surface area, we calculate how much the entanglement entropy changes under a double-trace deformation of a holographic CFT. In the AdS3/CFT2 setup, our result agrees with the known result in 2d CFTs. In higher dimensions, our results offer holographic predictions.
Large $N$ conformal field theories often admit unitary renormalization group flows triggered by double-trace deformations. We compute the change in scalar four-point functions under double-trace flow, to leading order in $1/N$. This has a simple dual in AdS, where the flow is implemented by a change of boundary conditions, and provides a physical interpretation of single-valued conformal partial waves. We extract the change in the conformal dimensions and three-point coefficients of infinite families of double-trace composite operators. Some of these quantities are found to be sign-definite un…
This work is an extension of our previous work [1] where we exploited holography to compute the complexity characteristics of Little String Theory (LST), a nonlocal, nongravitational field theory which flows to a local 2d CFT in the IR under RG via an integrable irrelevant (TT) deformation. Here we look at the more general LST obtained by UV deforming the 2d CFT by incorporating Lorentz violating irrelevant JT and TJ deformations on top of TT deformation, in an effort to capture the novel signatures of Lorentz violation (on top of nonlocality) on quantum complexity. In anticipation of the fact…
In this paper, we consider double trace deformation to single CFT${}_2$, and study time evolution after the deformation. The double trace deformation we consider is nonlocal: composed of two local operators placed at separate points. We study two types of local operators: one is usual local operator in CFT, and the other is HKLL bulk local operator, which is still operator in CFT but has properties as bulk local operator. We compute null energy and averaged null energy in the bulk in both types of deformations. We confirmed that, with the suitable choice of couplings, averaged null energies ar…
We study the UV dynamics of $μT \bar T$ deformed conformal field theories formulated as a deformation of generating functions. We explore the issue of non-perturbative completion of the $μ$ expansion by deriving an integral expression using the Fourier/Legendre transform technique, and show that it is more natural to impose Neumann, as opposed to the Dirichlet, boundary condition, for the metric at the cut-off surface recently proposed by McGough, Mezei, and Verlinde. We also comment on interesting connection to boundary conformal field theories.
We study wavefunctions of heavy scalars on de Sitter spacetime and their implications to dS/CFT correspondence. In contrast to light fields in the complementary series, heavy fields in the principal series oscillate outside the cosmological horizon. As a consequence, the quadratic term in the wavefunction does not follow a simple scaling and so it is hard to identify it with a conformal two-point function. In this paper, we demonstrate that it should be interpreted as a two-point function on a cyclic RG flow which is obtained by double-trace deformations of the dual CFT. This is analogous to t…
After turning on an interaction that couples the two boundaries of an eternal BTZ black hole, we find a quantum matter stress tensor with negative average null energy, whose gravitational backreaction renders the Einstein-Rosen bridge traversable. Such a traversable wormhole has an interesting interpretation in the context of ER=EPR, which we suggest might be related to quantum teleportation. However, it cannot be used to violate causality. We also discuss the implications for the energy and holographic entropy in the dual CFT description.
We consider a possible `deformation' of the trace of the heat kernel on odd dimensional spheres, motivated by the calculation of the free energy of a scalar field on a discretized circle. By using an expansion in terms of the modified Bessel functions, we obtain the values of the free energies after a suitable regularization.
In recent years, there have been two independent but related developments in the study of irrelevant deformations in two dimensional quantum field theories (QFTs). The first development is the deformation of a two dimensional QFT by the determinant of the energy momentum stress tensor, commonly referred to as $T{\bar T}$ deformation. The second development is in two dimensional holographic field theories which are dual to string theory in asymptotically Anti-de Sitter (AdS) spacetimes. In this latter development, the deformation is commonly referred to as single-trace $T{\bar T}$ deformation. …
Stochastic quantization and holographic Wilsonian renormalization group of scalar theory with generic mass, self-interaction and multiple trace deformation
Very special $T\bar{J}$ deformations of a conformal field theory are irrelevant deformations that break the Lorentz symmetry but preserve the twisted Lorentz symmetry. We construct a holographic description of very special $T\bar{J}$ deformations. We give a holographic recipe to study the double trace as well as single trace deformations. The former is obtained from the change of the boundary condition while the latter is obtained from the change of the supergravity background.
Recent results applying resurgence theory to finite-temperature field theories yield a detailed analytic structure determined by topological excitations. We examine finite-temperature SU(N) lattice gauge theories in light of these results. Double-trace Polyakov loop deformations move through different regions of the confined phase characterized by continuous change in the adjoint Polyakov loop. Lattice models show how the behavior of monopole constituents of calorons can change in the different confining regions. We conjecture that the pure SU(N) gauge theory is close to a special symmetric po…
Scalar fields on the bulk side of AdS/CFT correspondence can be assigned unconventional boundary conditions, related to the conventional one by Legendre transform. One can further perform double trace deformations which relate the two boundary conditions via renormalization group flow. Thinking of these operators as $S$ and $T$ transformations, respectively, we explore the $SL(2,{\bf R})$ family of models which naively emerges from repeatedly applying these operations. Depending on the parameters, the effective masses vary and can render the theory unstable. However, unlike in the $SL(2,{\bf Z…
Traversable wormhole with double trace deformations via gravitational shear and sound channels
Institut Teknologi Bandung（万隆理工学院）；National Research and Innovation Agency (BRIN)（国家研究与创新署）；Asia Pacific Center for Theoretical Physics, Pohang University of Science and Technology（韩国科学技术院亚太理论物理中心）；Indonesia Center for Theoretical and Mathematical Physics (ICTMP), Institut Teknologi Bandung（万隆理工学院印尼理论与数学物理中心）
Double trace deformations, that is products of two local operators, define perturbations of conformal field theories that can be studied exactly in the large-N limit. Even when the double trace deformation is irrelevant in the infrared, it is believed to flow to an ultraviolet fixed point. In this note we define the Kallen-Lehmann representation of the two-point function of a local operator O in a theory perturbed by the square of such operator. We use such representation to discover potential pathologies at intermediate points in the flow that may prevent to reach the UV fixed point. We apply…
We examine the AdS-CFT dual of arbitrary (non)supersymmetric fermionic mass deformations of N=4 SYM, and investigate how the backreaction of the RR and NS-NS two-form potentials dual to the fermion masses contribute to Coulomb-branch potential of D3 branes, which we interpret as the bulk boson mass matrix. Using representation-theory and supergravity arguments we show that the fermion masses completely determine the trace of this matrix, and that on the other hand its traceless components have to be turned on as non-normalizable modes. Our result resolves the tension between the belief that th…
We study thermodynamic aspects of a tractable toy model of holography for extremal Kerr black holes proposed in [arXiv:1806.10127]. On the gravity side, the theory can be described by the worldsheet action of string theory on a warped AdS$_3$ background supported by NS-NS flux. Once we turn on temperature, the deformed background is described by a black string solution of type IIB supergravity that features a locally warped AdS$_3$ factor. The dual field theory is conjectured to be a single-trace version of a $J\bar{T}$-deformed CFT at finite temperature. As evidence for the correspondence we …
We build a holographic model for the pairing fluctuation pseudogap phase in fermionic high temperature superconductivity/superfluidity based on the BCS-BEC crossover scenario. The pseudogap originates from incoherent Cooper pairing and has been observed in recent cold atom experiments. The strength of Cooper pairing and hence the BCS-BEC crossover is controlled by an effective 4-Fermi interaction and we argue that the double-trace deformation for charged scalar operator is a close analog in large N field theories. We employ the double-trace deformed Abelian Higgs model of holographic supercond…
We consider $\mathcal N=2$ $SU(2)$ gauge theories in four dimensions (pure or mass deformed) and discuss the properties of the simplest chiral observables in the presence of a generic $Ω$-deformation. We compute them by equivariant localization and analyze the structure of the exact instanton corrections to the classical chiral ring relations. We predict exact relations valid at all instanton number among the traces $\langle\text{Tr}φ^{n}\rangle$, where $φ$ is the scalar field in the gauge multiplet. In the Nekrasov-Shatashvili limit, such relations may be explained in terms of the available q…
We show that the quantum critical point (QCP) between a diffusive metal and ferromagnetic (or antiferromagnetic) phases in the SYK chain has a gravitational description corresponding to the double-trace deformation in an AdS$_2$ chain. Specifically, by studying a double-trace deformation of a $Z_2$ scalar in an AdS$_2$ chain where the $Z_2$ scalar is dual to the order parameter in the SYK chain, we find that the susceptibility and renormalization group equation describing the QCP in the SYK chain can be exactly reproduced in the holographic model. Our results suggest that the infrared geometry…
The Keldysh formalism is capable of describing driven-dissipative dynamics of open quantum systems as nonunitary effective field theories that are not necessarily thermodynamical, thus often exhibiting new physics. Here, we introduce a general Keldysh action that maximally obeys Weinbergian constraints, including locality, Poincaré invariance, and two "$CPT$" constraints: complete positivity and trace preserving as well as charge, parity, and time reversal symmetry. We find that the perturbative Lindblad term responsible for driven-dissipative dynamics introduced therein has the natural form o…
In the first part of this thesis, we study form factors of general gauge-invariant local composite operators in $\mathcal{N}=4$ super Yang-Mills theory at various loop orders and for various numbers of external legs. We show how to use on-shell methods for their calculation and in particular extract the dilatation operator from the result. We also investigate the properties of the corresponding remainder functions. Moreover, we extend on-shell diagrams, a Graßmannian integral formulation and an integrability-based construction via R-operators to form factors, focussing on the chiral part of th…
