Bulk Scalars Research Articles

Towards the non-perturbative cosmological bootstrap

We study quantum field theory on a de Sitter spacetime dSd+1 background. Our main tool is the Hilbert space decomposition in irreducible unitary representations of its isometry group SO(d + 1, 1). As the first application of the Hilbert space formalism, we recover the Källen-Lehmann spectral decomposition of the scalar bulk two-point function. In the process, we exhibit a relation between poles in the corresponding spectral densities and the boundary CFT data. Moreover, we derive an inversion formula for the spectral density through analytical continuation from the sphere and use it to find the spectral decompisiton for a few examples. Next, we study the conformal partial wave decomposition of the four-point functions of boundary operators. These correlation functions are very similar to the ones of standard conformal field theory, but have different positivity proper- ties that follow from unitarity in de Sitter. We conclude by proposing a non-perturbative conformal bootstrap approach to the study of these late-time four-point functions, and we illustrate our proposal with a concrete example for QFT in dS2.

Moduli stabilization with bulk scalar in nested doubly warped braneworld model

We examine the modulus stabilization mechanism of a warped geometry model with nested warping. Such a model with multiple moduli is known to offer a possible resolution of the fermion mass hierarchy problem in the Standard Model. A six dimensional doubly warped braneworld model under consideration admits two distinct moduli, with the associated warp factors dynamically generating different physical mass scales on four 3-branes. In order to address the hierarchy problem related to the Higgs mass, both moduli need to be stabilized around their desired values without any extreme fine tuning of parameters. We show that it is possible to stabilize them simultaneously due to the appearence of an effective 4D moduli potential, which is generated by a single massive bulk scalar field having non-zero VEVs frozen on the 3-branes. This gives rise to two scalar radions, one of which has mass slightly below {mathcal {O}}(TeV) and couplings to SM fields proportional to the inverse of its {mathcal {O}}(TeV) VEV, and the other has nearly {mathcal {O}}(M_{Pl}) mass and interactions with SM fields suppressed by the Planck scale. We also discuss how the entire mechanism can possibly be understood from a purely gravitational point of view, with higher curvature f(R) contributions in the bulk automatically providing a scalar degree of freedom that can serve as the stabilizing field in the Einstein frame.

Holographic models of composite Higgs in the Veneziano limit. Part II. Fermionic sector

We continue our study of strongly-coupled, approximately scale-invariant gauge theories with a large number of flavours, which provide a suitable ultraviolet completion of the composite-Higgs scenario. We identify the requisite operators to realise partial compositeness of the Standard-Model fermions. In order to compute the spectrum of composite fermionic states, we extend the bottom-up holographic models, which we previously introduced to capture the main features of the non-perturbative dynamics in the Veneziano limit, by adding fermion fields in the bulk. We identify regions in parameter space where some fermionic bound states become light, depending in particular on the number of flavours, the operator scaling dimensions, and the bulk Yukawa couplings. We also observe a dense spectrum of states, when multi-scale dynamics is induced by a large backreaction of bulk scalars on the geometry. Adapting the formalism of the holographic Wilsonian renormalisation group, we study the linear coupling between the composite and elementary fermions, as a function of energy scale. We find that, in some circumstances, the associated operators are dangerously irrelevant: the renormalisation-group flow gives rise to a large linear coupling in the infrared, even when it is irrelevant from the point of view of the ultraviolet fixed point. We finally compute the partially composite spectrum, correlate it with the analysis of the flow, and assess the potential phenomenological implications, e.g. for the top-quark partners.

From Feynman graphs to Witten diagrams

We investigate the possibility of generalizing Gopakumar’s microscopic derivation of Witten diagrams in large N free quantum field theory [1] to interacting theories. For simplicity we consider a massless, matrix valued real scalar field with Φh interaction in d-dimensions. Using Schwinger’s proper time formulation and organizing the sum over Feynman graphs by the number of loops l, we show that the two-point function can be expressed as a sum over boundary-to-boundary propagators of bulk scalars in AdS d+1 with mass determined by l.This manuscript is intended as a contribution to the festschrift of prof. Tekin Dereli’s on the occasion of his 72nd birthday.1

Holographic axion model: A simple gravitational tool for quantum matter

This is a complete and exhaustive review on the so-called holographic axion model -- a bottom-up holographic system characterized by the presence of a set of shift symmetric scalar bulk fields whose profiles are taken to be linear in the spatial coordinates. This simple model implements the breaking of translational invariance of the dual field theory by retaining the homogeneity of the background geometry and therefore allowing for controllable and fast computations. The usages of this model are very vast and they are a proof of the spectacular versatility of the framework. In this review, we touch upon all the up-to-date aspects of this model from its connection with massive gravity and effective field theories, to its role in modeling momentum dissipation and elastic properties ending with all the phenomenological features and its hydrodynamic description. In summary, this is a complete guide to one of the most used model in Applied Holography and a must-read for any researcher entering this field.

Bounds on Regge growth of flat space scattering from bounds on chaos

We study four-point functions of scalars, conserved currents, and stress tensors in a conformal field theory, generated by a local contact term in the bulk dual description, in two different causal configurations. The first of these is the standard Regge configuration in which the chaos bound applies. The second is the ‘causally scattering configuration’ in which the correlator develops a bulk point singularity. We find an expression for the coefficient of the bulk point singularity in terms of the bulk S matrix of the bulk dual metric, gauge fields and scalars, and use it to determine the Regge scaling of the correlator on the causally scattering sheet in terms of the Regge growth of this S matrix. We then demonstrate that the Regge scaling on this sheet is governed by the same power as in the standard Regge configuration, and so is constrained by the chaos bound, which turns out to be violated unless the bulk flat space S matrix grows no faster than s2 in the Regge limit. It follows that in the context of the AdS/CFT correspondence, the chaos bound applied to the boundary field theory implies that the S matrices of the dual bulk scalars, gauge fields, and gravitons obey the Classical Regge Growth (CRG) conjecture.

Deflation of vacuum energy during inflation due to Bulk-Brane interaction

We consider a brane world inflationary model in which inflation is driven by dynamics of a self-interacting scalar field living in the five-dimensional bulk. The scalar field is non-minimally coupled to matter fields on the brane and acts as an inflaton which induces a slow-roll inflation. We show that although the Friedmann equation is modified at early times due to effects of the extra dimension, the slow-roll condition is the same as that of the four-dimensional case. Due to the non-minimal coupling of matter with the bulk scalar, there is an energy transfer between the two components. We investigate the conditions under which the direction of this energy transfer can be from matter onto the bulk scalar. There are at least two advantages in this case. 1) It establishes a mechanism by which a large effective cosmological term on the brane is deflated during the inflation period. 2) The energy flow onto the bulk inflaton gives a more strongly damped evolution of the scalar field in the slow-roll region for a given potential. We then show that our results are supported by numerical estimations with quadratic and exponential potentials.

Holography on tessellations of hyperbolic space

We compute boundary correlation functions for scalar fields on tessellations of two- and three-dimensional hyperbolic geometries. We present evidence that the continuum relation between the scalar bulk mass and the scaling dimension associated with boundary-to-boundary correlation functions survives the truncation of approximating the continuum hyperbolic space with a lattice.

Local SU(2) \xd7 U(1) quark flavor symmetry in the RS bulk

We propose a model of quark flavor based on an additional SU(2) × U(1) local symmetry in a warped extra dimensional bulk. In contrast to other works, we break the additional gauge symmetry in the bulk via two complex scalars which acquire bulk vevs, rather than relying on brane-localized symmetry breaking. A gauge-covariant Kaluza-Klein decomposition of a theory with a bulk spontaneously broken gauge symmetry is performed, and exact expressions for the bulk profiles of all physical particles in such systems are given. The SM quark masses and mixings are then recreated using gauge-covariant bulk quark mass terms and Yukawa-like couplings to the new bulk scalars. A numerical sampling of points in the model parameter space that recreate the quark masses and mixings is performed at a KK scale of MKK = 5 TeV. We then compute the ∆F = 2 4-quark operators arising from our new flavor gauge bosons and scalars, and those arising from Kaluza-Klein modes of SM gauge bosons. By decoupling one of our bulk scalar fields to all quark fields except the right-handed up-like sector, we find that it is possible to greatly suppress tree-level contributions to the highly constrained Kaon mixing parameters. Instead, the dominant constraints on the model emerge from neutral Bd and D meson mixing. These constraints are explored with our numerical sampling of the model parameter space, and the specific contribution of the new flavor gauge bosons and scalars is discussed. We find that for a significant range of realistic flavor gauge couplings, the new gauge bosons compete with the normally dominant gluon flavor-changing currents, but flavor-changing operators emerging from the bulk scalar fields are highly suppressed. Finally, we briefly comment on flavor constraints that are independent of the flavor gauge sector arising from the Z{overline{b}}_L{b}_L coupling and rare top decays.

Dynamical origin of fermion bulk masses in a warped extra dimension

Extensions of the Standard Model featuring a warped extra dimension compactified on an S1/ℤ2 orbifold, in which the fermions and gauge bosons live in the bulk of the fifth dimension, offer one of the most compelling mechanisms for addressing both the hierarchy problem and the flavor puzzle of the Standard Model. However, the five-dimensional mass terms of bulk fermions must be odd functions on the orbifold, and as such they should be described by a field depending on the coordinate of the extra dimension. We demonstrate the feasibility of dynamically generating these fermion bulk masses with a bulk scalar field in warped extra dimensions. The bulk scalar acquires a vacuum expectation value, which is odd under the orbifold symmetry and gives rise to the fermion bulk masses through non-universal Yukawa-like interactions. Like in the conventional Randall-Sundrum setup, the localization of the different fermion zero modes along the extra dimension naturally explains the observed flavor structure and four-dimensional mass hierarchy of the SM fermions. We study the phenomenological implications of the backreaction on the metric and the modified fermion profiles due to the bulk scalar field on electroweak precision and flavor observables. Using up-to-date data, we show that the contributions to the S, T, and ϵK parameters require the mass of the first Kaluza-Klein gluon resonance to be of order 14 and 10 TeV in the minimal and the custodial model, respectively, regardless of the effect of the backreaction. Furthermore, effective flavor-changing interactions among the SM fermions induced by the bulk scalar are discussed. We also comment on the potential impact of the Higgs portal interaction of the bulk scalar on the couplings of the Higgs boson.

Recursion relations in p -adic Mellin Space

In this work, we formulate a set of rules for writing down p -adic Mellin amplitudes at tree-level. The rules lead to closed-form expressions for Mellin amplitudes for arbitrary scalar bulk diagrams. The prescription is recursive in nature, with two different physical interpretations: one as a recursion on the number of internal lines in the diagram, and the other as reminiscent of on-shell BCFW recursion for flat-space amplitudes, especially when viewed in auxiliary momentum space. The prescriptions are proven in full generality, and their close connection with Feynman rules for real Mellin amplitudes is explained. We also show that the integrands in the Mellin–Barnes representation of both real and p -adic Mellin amplitudes, the so-called pre-amplitudes, can be constructed according to virtually identical rules, and that these pre-amplitudes themselves may be re-expressed as products of particular Mellin amplitudes with complexified conformal dimensions.

Holographic Weyl anomaly for GJMS operators: one Laplacian to rule them all

The holographic Weyl anomaly for GJMS operators (or conformal powers of the Laplacian) are obtained in four and six dimensions. In the context of AdS/CFT correspondence, free conformal scalars with higher-derivative kinetic operators are induced by an ordinary second-derivative massive bulk scalar. At one-loop quantum level, the duality dictionary for partition functions entails an equality between the functional determinants of the corresponding kinetic operators and, in particular, it provides a holographic route to their Weyl anomalies. The heat kernel of a single bulk massive scalar field encodes the Weyl anomaly (type-A and type-B) coefficients for the whole tower of GJMS operators whenever they exist, as in the case of Einstein manifolds where they factorize into product of Laplacians.While a holographic derivation of the type-A Weyl anomaly was already worked out some years back, in this note we compute holographically (for the first time to the best of our knowledge) the type-B Weyl anomaly for the whole family of GJMS operators in four and six dimensions. There are two key ingredients that enable this novel holographic derivation that would be quite a daunting task otherwise: (i) a simple prescription for obtaining the holographic Weyl anomaly for higher-curvature gravities, previously found by the authors, that allows to read off directly the anomaly coefficients from the bulk action; and (ii) an implied WKB-exactness, after resummation, of the heat kernel for the massive scalar on a Poincaré-Einstein bulk metric with an Einstein metric on its conformal infinity.The holographically computed Weyl anomaly coefficients are explicitly verified on the boundary by exploiting the factorization of GJMS operators on Einstein manifolds and working out the relevant heat kernel coefficient.

A Truncation of 11‐Dimensional Supergravity for Fubini‐Like Instantons in AdS4/CFT3

AbstractFrom a consistent Kaluza‐Klein truncation of 11‐dimensional supergravity over , with a general 4‐form ansatz, we arrive at a set of equations and solutions for the included fields. In particular, we have a bulk equation for a self‐interacting (pseudo)scalar with arbitrary mass. By computing the energy‐momentum tensors of the associated Einstein equations, to include the backreaction, and setting them to zero, we solve the resulting equations with the bulk one and get solutions corresponding to marginal and marginally relevant deformations of the boundary CFT3, which break the conformal symmetry. These bulk (pseudo)scalars are ‐singlet and the corresponding solutions break all supersymmetries and parity because of the associated (anti)M‐branes wrapping around specific and mixed internal and external directions. As a result and according to AdS4/CFT3 duality rules, we would realize the boundary counterpart in three‐dimensional Chern‐Simon field theories with matters in fundamental representations. In particular, we build a ‐invariant Fubini‐like instanton solution by setting a specific boundary Lagrangian. The resulting solution is used to describe the dynamics of thin‐wall bubbles that cause instability and big crunch singularities in the bulk because of the unboundedness of the boundary double‐hump potential from below. Relations to mass‐deformed ABJM model, vector models and scale invariance breaking are also discussed. Meanwhile, we evaluate corrections for the background actions because of the bulk and boundary instantons.

Scalar fields on pAdS

We obtain a subgroup of the isometry group of pAdS (a p-adic version of AdS alternative to the Bruhat–Tits tree). We propose a candidate for the scalar bulk action and equation of motion on pAdS, and work out analytical expressions of the Green's functions for a particular choice of parameter together with an ansatz for general cases. The limiting behaviors of the Green's function are also studied. With their help, the convergence of small loops (whose radii are smaller than AdS length scale of pAdS) is analyzed.

Coadjoint orbit action of Virasoro group and two-dimensional quantum gravity dual to SYK/tensor models

The Nambu-Goldstone (NG) bosons of the SYK model are described by a coset space Diff/SL(2, ℝ), where Diff, or Virasoro group, is the group of diffeomorphisms of the time coordinate valued on the real line or a circle. It is known that the coadjoint orbit action of Diff naturally turns out to be the two-dimensional quantum gravity action of Polyakov without cosmological constant, in a certain gauge, in an asymptotically flat spacetime. Motivated by this observation, we explore Polyakov action with cosmological constant and boundary terms, and study the possibility of such a two-dimensional quantum gravity model being the AdS dual to the low energy (NG) sector of the SYK model. We find strong evidences for this duality: (a) the bulk action admits an exact family of asymptotically AdS2 spacetimes, parameterized by Diff/SL(2, ℝ), in addition to a fixed conformal factor of a simple functional form; (b) the bulk path integral reduces to a path integral over Diff/SL(2, ℝ) with a Schwarzian action; (c) the low temperature free energy qualitatively agrees with that of the SYK model. We show, up to quadratic order, how to couple an infinite series of bulk scalars to the Polyakov model and show that it reproduces the coupling of the higher modes of the SYK model with the NG bosons.

Marginal deformations of 3d supersymmetric U(N) model and broken higher spin symmetry

We examine the marginal deformations of double-trace type in 3d supersymmetric U(N) model with N complex free bosons and fermions. We compute the anomalous dimensions of higher spin currents to the 1/N order but to all orders in the deformation parameters by mainly applying the conformal perturbation theory. The 3d field theory is supposed to be dual to 4d supersymmetric Vasiliev theory, and the marginal deformations are argued to correspond to modifying boundary conditions for bulk scalars and fermions. Thus the modification should break higher spin gauge symmetry and generate the massesof higher spin fields. We provide supports for the dual interpretation by relating bulk computation in terms of Witten diagrams to boundary one in conformal perturbation theory.

Explicit reconstruction of the entanglement wedge

The problem of how the boundary encodes the bulk in AdS/CFT is still a subject of study today. One of the major issues that needs more elucidation is the problem of subregion duality; what information of the bulk a given boundary subregion encodes. Although the proof given by Dong, Harlow, and Wall [14] states that the entanglement wedge of the bulk should be encoded in boundary subregions, no explicit procedure for reconstructing the entanglement wedge was given so far. In this paper, mode sum approach to obtaining smearing functions for a single bulk scalar is generalised to include bulk reconstruction in the entanglement wedge of boundary subregions. It is generally expectated that solutions to the wave equation on a complicated coordinate patch are needed, but this hard problem has been transferred to a less hard but tractable problem of matrix inversion.

Explicitly broken supersymmetry with exactly massless moduli

There is an avatar of the little hierarchy problem of the MSSM in 3-dimensional supersymmetry. We propose a solution to this problem in AdS$_3$ based on the AdS/CFT correspondence. The bulk theory is a supergravity theory in which U(1) $\times$ U(1) R-symmetry is gauged by Chern-Simons fields. The bulk theory is deformed by a boundary term quadratic in the gauge fields. It breaks SUSY completely and sources an exactly marginal operator in the dual CFT. SUSY breaking is communicated by gauge interactions to bulk scalar fields and their spinor superpartners. Since the R-charges of scalar and spinor differ, this generates a SUSY breaking shift of their masses. The Ward identity facilitates the calculation of these mass shifts to any desired order in the strength of the deformation. Moduli fields are massless $R$-neutral bulk scalars with vanishing potential in the undeformed theory. These properties are maintained to all orders in the deformation despite the fact that moduli couple in the bulk to loops of R-charged fields.

Chasing the cuprates with dilatonic dyons

Magnetic field and momentum dissipation are key ingredients in describing condensed matter systems. We include them in gauge/gravity and systematically explore the bottom-up panorama of holographic IR effective field theories based on bulk Einstein-Maxwell Lagrangians plus scalars. The class of solutions here examined appear insufficient to capture the phenomenology of charge transport in the cuprates. We analyze in particular the temperature scaling of the resistivity and of the Hall angle. Keeping an open attitude, we illustrate weak and strong points of the approach.

Towards Kaluza-Klein Dark Matter on nilmanifolds

We present a first study of the field spectrum on a class of negatively-curved compact spaces: nilmanifolds or twisted tori. This is a case where analytical results can be obtained, allowing to check numerical methods. We focus on the Kaluza-Klein expansion of a scalar field. The results are then applied to a toy model where a natural Dark Matter candidate arises as a stable massive state of the bulk scalar.