Holographic RG Flows Research Articles

Euclidean wormholes in holographic RG flows

We describe a one-parameter family of Euclidean wormhole solutions with the topology of a compact hyperbolic space times an interval in Einstein gravity minimally coupled to a massless scalar field in AdSd+1 commonly referred to as Einstein-dilaton gravity. These solutions are locally described by the same metric and dilaton profile as the single-boundary Janus domain wall solutions in the same theory which are usually studied in the context of holographic RG flows. The wormholes compute the averaged product of partition functions of CFTs on either boundary deformed by different marginal couplings to the scalar operator dual to the dilaton. We observe that the renormalised volumes of these wormholes increase monotonically with the difference in the marginal couplings on the boundary thereby showing that the pair of CFTs on the boundaries get increasingly decorrelated as the difference in the marginal couplings increases. We use the partition functions of the three-dimensional wormhole solutions to determine the variance of the OPE data of local operators between the marginally deformed 2d CFTs and quantify how the variance decays with the difference in marginal couplings. In addition, a family of wormholes sourced by a thin shell of dust determine how the variance of the matrix elements of the dual line defect decays with the difference in marginal couplings. Applying the GKPW dictionary to wormholes, we compute averages of integrated dilaton correlators treating the wormhole amplitude as a functional of the dilaton sources. We observe that the crossed two-point correlators with a dilaton insertion on either boundary decay monotonically with the difference in marginal couplings consistent with the observation that the CFTs increasingly decorrelate as the difference in marginal couplings grows.

Explicit entropic proofs of irreversibility theorems for holographic RG flows

We revisit the existence of monotonic quantities along renormalization group flows using only the Null Energy Condition and the Ryu-Takayanagi formula for the entanglement entropy of field theories with anti-de Sitter gravity duals. In particular, we consider flows within the same dimension and holographically reprove the c-, F -, and a-theorems in dimensions two, three, and four. We focus on the family of maximally spherical entangling surfaces, define a quasi-constant of motion corresponding to the breaking of conformal invariance, and use a properly defined distance between minimal surfaces to construct a holographic c-function that is monotonic along the flow. We then apply our method to the case of flows across dimensions: there, we reprove the monotonicity of flows from AdSD+1 to AdS3 and prove the novel case of flows from AdS5 to AdS4.

Discontinuity in RG flows across dimensions: entanglement, anomaly coefficients and geometry

We study the entanglement entropy associated with a holographic RG flow from AdS7 to AdS4 × ℍ3, where ℍ3 is a 3-dimensional hyperbolic manifold with curvature κ. The dual six-dimensional RG flow is disconnected from Lorentz-invariant flows. In this context we address various notions of central charges and identify a monotonic candidate c-function that captures IR aspects of the flow. The UV behavior of the holographic entanglement entropy and, in particular its universal term, display an interesting dependence on the curvature, κ. We then contrast our holographic results with existing field theory computations in six dimensions and find a series of new corrections in curvature to the universal term in the entanglement entropy.

Correlation Functions in Holographic RG Flow of 3d Supergravity

Correlation Functions in Holographic RG Flow of 3d Supergravity

Holographic RG flows and boundary conditions in a 3D gauged supergravity

In this work we focus on the study of RG flows of conformal field theories that are holographically dual to Poincaré domain wall solutions in D=3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$D=3$$\\end{document}, N=(2,0)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {N}=(2,0)$$\\end{document} gauged supergravity coupled to a sigma model with target space SU(1,1)/U(1)=H2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extrm{SU}(1, 1)/\ extrm{U}(1) = \\mathbb {H}^2$$\\end{document}. This theory is truncated to a subsector where the vector field and phase of the scalar field vanish and we consider different boundary conditions for the remaining real scalar field. The RG flows, which are mostly non-superysymmetric, are analyzed by treating the supergravity field equations as a dynamical system for the scalar field and its derivative with respect to the scale factor. Phase diagrams are constructed for different values of the parameter a2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$a^2$$\\end{document}, which is related to the curvature of the scalar manifold. The behavior of solutions near the boundary is used to determine their type based on the expansion of the corresponding fake superpotential. By incorporating information on the boundary conditions, the obtained RG flows are interpreted using the holographic dictionary. Numerical solutions and plots of the fake superpotential are also provided.

Holographic a-functions and Boomerang RG flows

We use the radial null energy condition to construct a monotonic a-function for a certain type of non-relativistic holographic RG flows. We test our a-function in three different geometries that feature a Boomerang RG flow, characterized by a domain wall between two AdS spaces with the same AdS radius, but with different (and sometimes direction-dependent) speeds of light. We find that the a-function monotonically decreases and goes to a constant in the asymptotic regimes of the geometry. Using the holographic dictionary in this asymptotic AdS spaces, we find that the a-function not only reads the fixed point central charge but also the speed of light, suggesting what the correct RG charge might be for non-relativistic RG flows.

Holographic RG flows from four-dimensional N = 2 gauged supergravities

In quantum field theories, the examination of particle interactions is facilitated through the application of Feynman diagrams. The computation of loop Feynman diagrams often yields divergent or infinite values. To tackle this issue, a method known as renormalization is employed, which entails the removal of these infinities. The phenomenon of a physical system undergoing changes under different scales gives rise to a concept referred to as the renormalization group. Certain renormalization group trajectories, denoted as RG flows, describe transformations of a conformal field theory (CFT) into other conformal or non-conformal theories. These transformations result in deformations of a UV conformal fixed point into another fixed point or into a non-conformal phase within the infrared (IR) regime. In this study, we investigate holographic RG flows originating from N = 2 gauged supergravity with an SO(2) × SO(6) gauge group. These solutions delineate RG flows from the N = 2 CFT to a three-dimensional non-conformal field theory driven by mass deformations. This transformation is elucidated through the AdS/CFT correspondence, also known as AdS/CFT holography.

New supersymmetric AdS_5 black strings from 5D N=4 gauged supergravity

We find a large class of new supersymmetric AdS_5 black strings from five-dimensional N=4 gauged supergravity coupled to five vector multiplets with SO(2)_Dtimes SO(3)times SO(3) gauge group. These solutions have near horizon geometries of the form AdS_3times Sigma ^2 for Sigma ^2 being a two-sphere (S^2) or a hyperbolic space (H^2). There are four supersymmetric AdS_5 vacua with N=4 and N=2 supersymmetries. By performing topological twists along Sigma ^2 with SO(2)times SO(2)_{text {diag}} and SO(2)_{text {diag}} gauge fields, we find a number of AdS_3times Sigma ^2 fixed points describing near horizon geometries of black strings in asymptotically AdS_5 spaces. Most of the solutions take the form of AdS_3times H^2 with only one being AdS_3times S^2 preserving SO(2)_{text {diag}} symmetry. We also give the corresponding black string solutions interpolating between asymptotically locally AdS_5 vacua and the near horizon AdS_3times Sigma ^2 geometries. There are a number of solutions flowing from one, two or three AdS_5 vacua to an AdS_3times Sigma ^2 fixed point. These solutions can also be considered as holographic RG flows across dimensions from N=2 and N=1 SCFTs in four dimensions to two-dimensional SCFTs with N=(2,0) or N=(0,2) supersymmetry.

Stability analysis of holographic RG flows in 3d supergravity

Stability analysis of holographic RG flows in 3d supergravity

AdS_5 vacua and holographic RG flows from 5D N=4 gauged supergravity

We study five-dimensional N=4 gauged supergravity coupled to five vector multiplets with SO(2)_Dtimes SO(3)times SO(3) gauge group. There are four supersymmetric AdS_5 vacua in the truncation to SO(2)_{text {diag}} invariant scalars. Two of these vacua preserve the full N=4 supersymmetry with SO(2)_Dtimes SO(3)times SO(3) and SO(2)_Dtimes SO(3)_{text {diag}} symmetries. These have an analogue in N=4 gauged supergravity with SO(2)times SO(3)times SO(3) gauge group. The other two AdS_5 vacua preserve only N=2 supersymmetry with SO(2)_{text {diag}}times SO(3) and SO(2)_{text {diag}} symmetry. The former has an analogue in the previous study of SO(2)_Dtimes SO(3) gauge group while the latter is a genuinely new N=2AdS_5 vacuum. These vacua should be dual to N=2 and N=1 superconformal field theories (SCFTs) in four dimensions with different flavour symmetries. We give the full scalar mass spectra at all of the AdS_5 critical points which provide information on conformal dimensions of the dual operators. Finally, we study holographic RG flows interpolating between these AdS_5 vacua and find a new class of solutions. In addition to the RG flows from the trivial SO(2)_Dtimes SO(3)times SO(3)N=4 critical point, at the origin of the scalar manifold, to all the other critical points, there is a family of RG flows from the trivial N=4 critical point to the new SO(2)_{text {diag}}N=2 critical point that pass arbitrarily close to the SO(2)_Dtimes SO(3)_{text {diag}}N=4 critical point.

Holographic RG flows on Squashed S3

Holographic RG flows dual to QFTs on a squashed S3 are considered in the framework of Einstein dilaton gravity in four dimensions. A general dilaton potential is used and flows are driven by a scalar relevant operator. The general properties of such flows are analysed and the UV and IR asymptotics are computed. Exotic asymptotics are found, that are different from the standard Fefferman-Graham asymptotics.

C-functions in flows across dimensions

We explore the notion of c-functions in renormalization group flows between theories in different spacetime dimensions. We discuss functions connecting central charges of the UV and IR fixed point theories on the one hand, and functions which are monotonic along the flow on the other. First, using the geometric properties of the holographic dual RG flows across dimensions and the constraints from the null energy condition, we construct a monotonic holographic c-function and thereby establish a holographic c-theorem across dimensions. Second, we use entanglement entropies for two different types of entangling regions in a field theory along the RG flow across dimensions to construct candidate c-functions which satisfy one of the two criteria but not both. In due process we also discuss an interesting connection between corner contributions to the entanglement entropy and the topology of the compact internal space. As concrete examples for both approaches, we holographically study twisted compactifications of 4d mathcal{N} = 4 SYM and compactifications of 6d mathcal{N} = (2, 0) theories.

Page curves and bath deformations

We study the black hole information problem within a semiclassically gravitating AdS_dd black hole coupled to and in equilibrium with a dd-dimensional thermal conformal bath. We deform the bath state by a relevant scalar deformation, triggering a holographic RG flow whose "trans-IR" region deforms from a Schwarzschild geometry to a Kasner universe. The setup manifests two independent scales which control both the extent of coarse-graining and the entanglement dynamics when counting Hawking degrees of freedom in the bath. In tuning either, we find nontrivial changes to the Page time and Page curve. We consequently view the Page curve as a probe of the holographic RG flow, with a higher Page time manifesting as a result of increased coarse-graining of the bath degrees of freedom.

Holographic RG flows and symplectic deformations of N=4 gauged supergravity

We study four-dimensional $N=4$ gauged supergravity with $SO(4)\times SO(4)\sim SO(3)\times SO(3)\times SO(3)\times SO(3)$ gauge group in the presence of symplectic deformations. There are in general four electric-magnetic phases corresponding to each $SO(3)$ factor, but two phases of the $SO(3)$ factors embedded in the $SO(6)$ R-symmetry are fixed. One phase can be set to zero by $SL(2,\mathbb{R})$ transformations. The second one gives equivalent theories for any non-vanishing values and can be set to $\frac{\pi}{2}$ resulting in gauged supergravities that admit $N=4$ supersymmetric $AdS_4$ vacua. The remaining two phases are truely deformation parameters leading to different $SO(4)\times SO(4)$ gauged supergravities. As in the $\omega$-deformed $SO(8)$ maximal gauged supergravity, the cosmological constant and scalar masses of the $AdS_4$ vacuum at the origin of the scalar manifold with $SO(4)\times SO(4)$ symmetry do not depend on the electric-magnetic phases. We find $N=1$ holographic RG flow solutions between $N=4$ critical points with $SO(4)\times SO(4)$ and $SO(3)_{\textrm{diag}}\times SO(3)\times SO(3)$ or $SO(3)\times SO(3)_{\textrm{diag}}\times SO(3)$ symmetries. We also give $N=2$ and $N=1$ RG flows from these critical points to various non-conformal phases. However, contrary to the $\omega$-deformed $SO(8)$ gauged supergravity, there exist non-trivial supersymmetric $AdS_4$ critical points only for particular values of the deformation parameters within the scalar sectors under consideration.

Supersymmetric AdS_4 black holes from matter-coupled N=3,4 gauged supergravities

We study supersymmetric AdS_4 black holes in matter-coupled N=3 and N=4 gauged supergravities in four dimensions. In N=3 theory, we consider N=3 gauged supergravity coupled to three vector multiplets and SO(3)times SO(3) gauge group. The resulting gauged supergravity admits two N=3 supersymmetric AdS_4 vacua with SO(3)times SO(3) and SO(3) symmetries. We find an AdS_2times H^2 solution with SO(2)times SO(2) symmetry and an analytic solution interpolating between this geometry and the SO(3)times SO(3) symmetric AdS_4 vacuum. For N=4 gauged supergravity coupled to six vector multiplets with SO(4)times SO(4) gauge group, there exist four supersymmetric AdS_4 vacua with SO(4)times SO(4), SO(4)times SO(3), SO(3)times SO(4) and SO(3)times SO(3) symmetries. We find a number of AdS_2times S^2 and AdS_2times H^2 geometries together with the solutions interpolating between these geometries and all, but the SO(3)times SO(3), AdS_4 vacua. These solutions provide a new class of AdS_4 black holes with spherical and hyperbolic horizons dual to holographic RG flows across dimensions from N=3,4 SCFTs in three dimensions to superconformal quantum mechanics within the framework of four-dimensional gauged supergravity.

Revisiting Coleman-de Luccia transitions in the AdS regime using holography

Coleman-de Luccia processes for AdS to AdS decays in Einstein-scalar theories are studied. Such tunnelling processes are interpreted as vev-driven holographic RG flows of a quantum field theory on de Sitter space-time. These flows do not exist for generic scalar potentials, which is the holographic formulation of the fact that gravity can act to stabilise false AdS vacua. The existence of Coleman-de Luccia tunnelling solutions in a potential with a false AdS vacuum is found to be tied to the existence of exotic RG flows in the same potential. Such flows are solutions where the flow skips possible fixed points or reverses direction in the coupling. This connection is employed to construct explicit potentials that admit Coleman-de Luccia instantons in AdS and to study the associated tunnelling solutions. Thin-walled instantons are observed to correspond to dual field theories with a parametrically large value of the dimension ∆ for the operator dual to the scalar field, casting doubt on the attainability of this regime in holography. From the boundary perspective, maximally symmetric instantons describe the probability of symmetry breaking of the dual QFT in de Sitter. It is argued that, even when such instantons exist, they do not imply an instability of the same theory on flat space or on R × S3.

S-folds and holographic RG flows on the D3-brane

Type IIB S-folds of the form AdS4 × S1 × S5 are conjectured to correspond to new strongly coupled three-dimensional CFT’s on a localised interface of SYM4. In this work we construct holographic RG flows on the D3-brane that generically connect anisotropic deformations of SYM4 in the UV to various S-fold CFT’s in the IR with different amounts of supersymmetry and flavour symmetries. Examples of holographic RG flows between S-fold CFT’s are also presented. Lastly a geometric interpretation of axion deformations is provided in terms of monodromies on the internal S5 when moving around the S1. Special attention is paid to the monodromy-induced patterns of symmetry breaking as classified by the mapping torus Th(S5).

Holographic RG flows and Janus solutions from matter-coupled N=4 gauged supergravity

We study an SO(2)times SO(2)times SO(2)times SO(2) truncation of four-dimensional N=4 gauged supergravity coupled to six vector multiplets with SO(4)times SO(4) gauge group and find a new class of holographic RG flows and supersymmetric Janus solutions. In this truncation, there is a unique N=4 supersymmetric AdS_4 vacuum dual to an N=4 SCFT in three dimensions. In the presence of the axion, the RG flows generally preserve N=2 supersymmetry while the supersymmetry is enhanced to N=4 for vanishing axion. We find solutions interpolating between the AdS_4 vacuum and singular geometries with different residual symmetries. We also show that all the singularities are physically acceptable within the framework of four-dimensional gauged supergravity. Accordingly, the solutions are holographically dual to RG flows from the N=4 SCFT to a number of non-conformal phases in the IR. We also find N=4 and N=2 Janus solutions with SO(4)times SO(4) and SO(2)times SO(2)times SO(3)times SO(2) symmetries, respectively. The former is obtained from a truncation of all scalars from vector multiplets and can be regarded as a solution of pure N=4 gauged supergravity. On the other hand, the latter is a genuine solution of the full matter-coupled theory. These solutions describe conformal interfaces in the N=4 SCFT with N=(4,0) and N=(2,0) supersymmetries.

Constraining nonrelativistic RG flows with holography

We examine non-relativistic holographic RG flows by working with Einstein-Maxwell-scalar theories which support geometries that break Lorentz invariance at some energy scale. We adopt the superpotential formalism, which helps us characterize the radial flow in this setup and bring to light a number of generic features. In particular, we identify several quantities that behave monotonically under RG flow. As an example, we show that the index of refraction is generically monotonic. We also construct a combination of the superpotentials that flows monotonically in Einstein-scalar theories supporting non-relativistic solutions, and which reduces to the known c-function in the relativistic limit. Interestingly, such quantity also exhibits monotonicity in a variety of black hole solutions to the full Einstein-Maxwell-scalar theory, hinting at a deeper structure. Finally, we comment on the breakdown of such monotonicity conditions and on the relation to a candidate c-function obtained previously from entanglement entropy.

Holographic QFTs on S2\xd7S2, spontaneous symmetry breaking and Efimov saddle points

Holographic CFTs and holographic RG flows on space-time manifolds which are d-dimensional products of spheres are investigated. On the gravity side, this corresponds to Einstein-dilaton gravity on an asymptotically AdSd+1 geometry, foliated by a product of spheres. We focus on holographic theories on S2× S2, we show that the only regular five-dimensional bulk geometries have an IR endpoint where one of the sphere shrinks to zero size, while the other remains finite. In the Z2-symmetric limit, where the two spheres have the same UV radii, we show the existence of a infinite discrete set of regular solutions, satisfying an Efimov-like discrete scaling. The Z2-symmetric solution in which both spheres shrink to zero at the endpoint is singular, whereas the solution with lowest free energy is regular and breaks Z2 symmetry spontaneously. We explain this phenomenon analytically by identifying an unstable mode in the bulk around the would-be Z2-symmetric solution. The space of theories have two branches that are connected by a conifold transition in the bulk, which is regular and correspond to a quantum first order transition. Our results also imply that AdS5 does not admit a regular slicing by S2× S2.