We consider four-point functions of operators in the stress tensor multiplet of the 3d $\mathcal{N}=6$ $U(N)_k\times U(N+M)_{-k}$ or $SO(2)_{2k}\times USp(2+2M)_{-k}$ ABJ theories in the limit where $M$ and $k$ are taken to infinity while $N$ and $λ\sim M/k$ are held fixed. In this limit, these theories have weakly broken higher spin symmetry and are holographically dual to $\mathcal{N}=6$ higher spin gravity on $AdS_4$, where $λ$ is dual to the bulk parity breaking parameter. We use the weakly broken higher spin Ward identities, superconformal Ward identities, and the Lorentzian inversion formula to fully determine the tree level stress tensor multiplet four-point function up to two free parameters. We then use supersymmetric localization to fix both parameters for the ABJ theories in terms of $λ$, so that our result for the tree level correlator interpolates between the free theory at $λ=0$ and a parity invariant interacting theory at $λ=1/2$. We compare the CFT data extracted from this correlator to a recent numerical bootstrap conjecture for the exact spectrum of $U(1)_{2M}\times U(1+M)_{-2M}$ ABJ theory (i.e. $λ=1/2$ and $N=1$), and find good agreement in the higher spin regime.
We generalize the operators of ABJM theory, given by Schur polynomials, in ABJ theory by computing the two point functions in the free field and at finite $(N_1,N_2)$ limits. These polynomials are then identified with the states of the dual gravity theory. Further, we compute correlators among giant gravitons as well as between giant gravitons and ordinary gravitons through the corresponding correlators of ABJ(M) theory. Finally, we consider a particular non-trivial background produced by an operator with an $\cal R$-charge of $O(N^2)$ and find, in presence of this background, due to the contr…
We construct a class of operators, given by Schur polynomials, in ABJM theory. By computing two point functions at finite $N$ we confirm these are diagonal for this class of operators in the free field limit. We also calculate exact three and multi point correlators in the zero coupling limit. Finally, we consider a particular nontrivial background produced by an operator with an $R$-charge of $O(N^2$. We show that the nonplanar corrections (which can no longer be neglected, even at large $N$) can be resummed to give a $1/(N+M)$ expansion for correlators computed in this background.
We calculate fermionic response in domain wall backgrounds of four-dimensional gauged supergravity interpolating between distinct stable AdS vacua. The backgrounds, found by Bobev et al., are holographically dual to zero-temperature states of ABJM theory at finite density for monopole charge and are similar to zero-temperature limits of holographic superconductors, but with a symmetry-breaking source as well. The condensed scalar mixes charged and neutral fields dual to composite fermionic operators in the Dirac equations. Both gapped and gapless bands of stable quasiparticles are found.
In this work we consider various correlators with Schur polynomials in ABJ(M) models that on the dual gravity side should correspond to processes involving giant gravitons. Our analysis imposes several constraints on the physics of the probe branes on AdS4xCP3 as well as sheds more light on giant graviton solutions in this background with additional NS B-field. Our main tool is a formula that we derive for extremal n-point functions of the single trace chiral primary operators in the free field theory limit. The formula expresses the correlators in terms of the two-point function of Schur poly…
We study local operator insertions on 1/2-BPS line defects in ABJM theory. Specifically, we consider a class of four-point correlators in the CFT$_1$ with SU$(1, 1|3)$ superconformal symmetry defined on the 1/2-BPS Wilson line. The relevant insertions belong to the short supermultiplet containing the displacement operator and correspond to fluctuations of the dual fundamental string in AdS$_4 \times \mathbb{C}\textrm{P}^3$ ending on the line at the boundary. We use superspace techniques to represent the displacement supermultiplet and we show that superconformal symmetry determines the four-po…
We consider the U(1) charged sector of ABJM theory at finite temperature, which corresponds to the Reissner-Nordstrom AdS black hole in the dual type IIA supergravity description. Including back-reaction to the bulk geometry, we show that phase transitions occur to a broken phase where SU(4) R-symmetry of the field theory is broken spontaneously by the condensation of dimension one or two operators. We show both numerically and analytically that the relevant critical exponents for the dimension one operator agree precisely with those of mean field theory in the strongly coupled regime of the l…
We consider the four-point function of the lowest scalar in the stress-energy tensor multiplet in $\mathcal{N}=8$ ABJ(M) theory \cite{Aharony:2008ug, Aharony:2008gk}. At large central charge $c_T\sim N^{3/2}$, this correlator is given by the corresponding holographic correlation function in 11d supergravity on $AdS_4\times S^7$. We use Mellin space techniques to compute the leading $1/c_T$ correction to anomalous dimensions and OPE coefficients of operators that appear in this holographic correlator. For half and quarter-BPS operators, we find exact agreement with previously computed localizat…
Facultad de Ingeniería, Universidad San Sebastián（圣塞巴斯蒂安大学工程学院）；Dipartimento di Fisica, Università degli Studi di Milano–Bicocca and INFN, Sezione di Milano–Bicocca（米兰比可卡大学物理系及意大利国家核物理研究所米兰比可卡分部）；International Institute of Physics, Federal University of Rio Grande do Norte（北里奥格兰德联邦大学国际物理研究所）
We study graviton scattering on $AdS_4\times S^7$, which is dual to the stress tensor multiplet four-point function in the maximally supersymmetric 3d $U(N)_1\times U(N)_{-1}$ ABJM theory. We compute 1-loop corrections to this holographic correlator coming from Witten diagrams with supergravity $R$ and higher derivative $R^4$ vertices, up to contact term ambiguities, and find that the flat space limit matches the corresponding terms in the 11d M-theory S-matrix. We then use supersymmetric localization to show that all the 1-loop contact terms vanish, as was previously observed for the $AdS_4\t…
We study n-point correlation functions for chiral primary operators in three dimensional supersymmetric Chern-Simons matter theories. Our analysis is carried on in N=2 superspace and covers N=2,3 supersymmetric CFT's, the N=6 ABJM and the N=8 BLG models. In the limit where the positions of adjacent operators become light-like, we find that the one-loop n-point correlator divided by its tree level expression coincides with a light-like n-polygon Wilson loop. Remarkably, the result can be simply expressed as a linear combination of five dimensional two-mass easy boxes. We manage to evaluate the …
In this work, building up on [1] we present momentum space Ward identities related to broken higher spin symmetry as an alternate approach to computing correlators of spinning operators in interacting theories such as the quasi-fermionic and quasi-bosonic theories. The direct Feynman diagram approach to computing correlation functions is intricate and in general has been performed only in specific kinematic regimes. We use higher spin equations to obtain the parity even and parity odd contributions to two-, three- and four-point correlators involving spinning and scalar operators in a general …
We explore a class of CFT's with higher spin currents and charges. Away from the free or $N=\infty$ limit the non-conservation of currents is governed by operators built out of the currents themselves, which deforms the algebra of charges by, and together with, its action on the currents. This structure is encoded in a certain $A_\infty/L_\infty$-algebra. Under quite general assumptions we construct invariants of the deformed higher spin symmetry, which are candidate correlation functions. In particular, we show that there is a finite number of independent structures at the $n$-point level. Th…
Using the AdS/CFT correspondence we study vacua of N=4 SYM for which part of the gauge symmetry is broken by expectation values of scalar fields. A specific subclass of such vacua can be analyzed with gauged supergravity and the corresponding domain wall solutions lift to continuous distributions of D3-branes in type IIB string theory. Due to the non-trivial expectation value of the scalars, the SO(6) R-symmetry is spontaneously broken and field theory predicts the existence of Goldstone bosons. We explicitly show that, in the dual supergravity description, these emerge as massless poles in th…
We present a constructive derivation of holographic four-point correlators of arbitrary half-BPS operators for all maximally supersymmetric conformal field theories in $d>2$. This includes holographic correlators in 3d ${\cal N}=8$ ABJM theories, 4d ${\cal N}=4$ SYM theory and the 6d ${\cal N}=(2,0)$ theory, dual to tree-level amplitudes in 11D supergravity on $AdS_4 \times S^7$, 10D supergravity on $AdS_5 \times S^5$ and 11D supergravity on $AdS_7 \times S^4$, respectively. We introduce the concept of Maximally R-symmetry Violating (MRV) amplitude, which corresponds to a special configuration…
Correlators of gauge invariant operators provide useful information on the dynamics, phases and spectra of a quantum field theory. In this paper, we consider N=1 supersymmetric theories and focus our attention on the supercurrent multiplet. We give a complete characterization of two-point functions of operators belonging to such multiplet, like the energy-momentum tensor and the supercurrent, and study the relations between them. We discuss instances of weakly coupled and strongly coupled theories, in which different symmetries, like conformal invariance and supersymmetry, may be conserved and…
It was recently shown that IIB supergravity on AdS$_5\times$S$^5$ enjoys 10d conformal symmetry and that superstring theory on this background can be described using a 10d scalar effective field theory. In this paper we adapt these two complementary approaches to correlators of hypermultiplets in AdS$_2\times$S$^2$. In particular, we show that 4-point correlators of $1/2$-BPS operators in the 1d boundary can be computed using 4d conformal symmetry and a 4d effective action in the bulk. The 4d conformal symmetry is realised by acting with Casimirs of $SU(1,1|2)$, and is generically broken by hi…
We compute current correlators of the CP^{N-1} field theory in 2+1 dimensions, both at the critical point and in the phase with spontaneously broken SU(N) symmetry. Universal constants are obtained to next-to-leading order in the 1/N expansion. Implications are noted for quantum critical points of antiferromagnets, and their vicinity.
We consider the four-point function of operators in the stress tensor multiplet of the $U(N)_k\times U(N)_{-k}$ ABJM theory, in the limit where $N$ is taken to infinity while $N/k^{5}$ is held fixed. In this limit, ABJM theory is holographically dual to type IIA string theory on $AdS_4\times \mathbb{CP}^3$ at finite string coupling $g_s \sim (N/k^5)^{1/4}$. While at leading order in $1/N$, the stress tensor multiplet four-point function can be computed from type IIA supergravity, in this work we focus on the first subleading correction, which comes from tree level Witten diagrams with an $R^4$…
School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）；Kavli Institute for Theoretical Sciences, University of Chinese Academy of Sciences（中国科学院大学理论科学卡弗里研究所）；Peng Huanwu Center for Fundamental Theory（彭桓武基础理论研究中心）
Using a novel relation between the parity even and odd parts of a correlator, we show that the 3-point function of conserved or weakly broken currents in 3d CFT can be obtained from just the free fermion (FF) or the free boson (FB) theory. In the special case of large $N$ Chern-Simons matter theories, we obtain the correlator in terms of a coupling constant dependent ``anyonic phase" factor. This anyonic phase factor was previously obtained in the $2\rightarrow 2$ exact S-matrix result and is consistent with strong-weak duality. By varying the coupling constant the CFT correlator interpolates …
We study correlators of R-symmetry currents in the Coulomb branch of N = 4 supersymmetric gauge theory in the large-N limit, using the AdS/CFT correspondence. In particular, we consider gauge fields in the presence of gravity and scalar fields parameterizing the coset SL(6,R)/SO(6) in the context of five-dimensional gauged supergravity. From a ten-dimensional point of view these backgrounds correspond to continuous D3-brane distributions. We find the surprising result that all 2-point functions of gauge currents fall into the same universality class, irrespectively of whether they correspond t…
Three-dimensional conformal field theories (CFTs) with slightly broken higher spin symmetry provide an interesting laboratory to study general properties of CFTs and their roles in the AdS/CFT correspondence. In this work we compute the four-point functions at arbitrary 't Hooft coupling $λ$ in the CFTs with slightly broken higher spin symmetry. We use a bootstrap approach based on the approximate higher spin Ward identity. We show that the bootstrap equation is separated into two parts with opposite parity charges, and it leads to a recursion relation for the $λ$ expansions of the correlation…
We study a renormalization group flow of ABJM theory embedded into the warped A_8 geometry and explore the dependence of the vacuum structure on the parameters of the theory. This model has a product group gauge structure U(N)xU(n+l) and comes equipped with discrete parameters N, l and k, a continuous parameter b related to the ratio of the Yang-Mills coupling for the two gauge groups, and one dimensionful parameter gYM^2 setting the overall scale. A supersymmetric supergravity solution exists when Q=N-l(l-k)/2k-k/24 is positive and is interpretable as a RG flow from a Yang-Mills like UV fixed…
Conformal symmetry has important consequences for strong interactions at short distances and provides powerful tools for practical calculations. Even if the Lagrangians of Quantum Chromodynamics (QCD) and Electrodynamics (QED) are invariant under conformal transformations, this symmetry is broken by quantum corrections. The signature of the symmetry breaking is encoded in the presence of massless poles in correlators involving stress-energy tensors. We present a general study of the correlation functions $\langle TJJ\rangle$ and $\langle TTJJ\rangle$ of conformal field theory (CFT) in the flat…
The local form of higher-spin equations found recently to the second order [1] is shown to properly reproduce the anticipated $AdS/CFT$ correlators for appropriate boundary conditions. It is argued that consistent $AdS/CFT$ holography for the parity-broken boundary models needs a nontrivial modification of the bosonic truncation of the original higher-spin theory with the doubled number of fields, as well as a nonlinear deformation of the boundary conditions in the higher orders.
We consider using broken superconformal symmetry and the super operator product expansion (sOPE) to constrain and analyze hidden sector theories that couple to our gauge forces and are not necessarily weakly coupled. Conformal and supersymmetry breaking are IR effects, associated with field or spurion expectation values, whereas the sOPE is determined in the UV and hence does not notice the breaking. The broken superconformal symmetry relates OPE coefficients of superconformal descendant operators to those of the superconformal primaries. We apply these ideas to the current correlators of gene…
We consider conformal field theories around points of large twist degeneracy. Examples of this are theories with weakly broken higher spin symmetry and perturbations around generalised free fields. At the degenerate point we introduce twist conformal blocks. These are eigenfunctions of certain quartic operators and encode the contribution, to a given four-point correlator, of the whole tower of intermediate operators with a given twist. As we perturb around the degenerate point, the twist degeneracy is lifted. In many situations this breaking is controlled by inverse powers of the spin. In suc…
We study fluctuations around the warped conifold supergravity solution of Klebanov and Tseytlin [hep-th/0002159], known to be dual to a cascading N=1 gauge theory. Although this supergravity background is not asymptotically AdS, corresponding to a non-conformal field theory, it is possible to apply the usual methods of AdS/CFT duality to extract the high energy behavior of field theory correlators by solving linearized equations of motion for fluctuations around the background. We consider the Goldstone vector dual to the anomalous R-symmetry current and compute its mass, which exactly matches…
The Sachdev-Ye-Kitaev (SYK) model, a theory of N Majorana fermions with q-body interactions, becomes in the large q limit a conformally-broken Liouville field theory. Taking this limit preserves many interesting properties of the model, yet makes the theory as a whole much more tractable. Accordingly, we produce novel expressions for the two and four-point correlators at arbitrary temperature and find the surprising result they take a universal closed form. We note that these expressions correctly match onto and interpolate between previously-obtained low-energy results and simple high-energy …
We apply the method of the large spin bootstrap to analyse fermionic conformal field theories with weakly broken higher spin symmetry. Through the study of correlators of composite operators, we find the anomalous dimensions and OPE coefficients in the Gross-Neveu model in $d=2+\varepsilon$ dimensions and the Gross-Neveu-Yukawa model in $d=4-\varepsilon$ dimensions, based only on crossing symmetry. Furthermore a non-trivial solution in the $d=2+\varepsilon$ expansion is found for a fermionic theory in which the fundamental field is not part of the spectrum. The results are perturbative in $\va…
Scattering amplitudes at weak coupling are highly constrained by Lorentz invariance, locality and unitarity, and depend on model details only through coupling constants and particle content. In this paper, we develop an understanding of inflationary correlators which parallels that of flat-space scattering amplitudes. Specifically, we study slow-roll inflation with weak couplings to extra massive particles, for which all correlators are controlled by an approximate conformal symmetry on the boundary of the spacetime. After classifying all possible contact terms in de Sitter space, we derive an…
During inflation, the geometry of spacetime is described by a (quasi-)de Sitter phase. Inflationary observables are determined by the underlying (softly broken) de Sitter isometry group SO(1, 4) which acts like a conformal group on R^3: when the fluctuations are on super-Hubble scales, the correlators of the scalar fields are constrained by conformal invariance. Heavy fields with mass m larger than the Hubble rate H correspond to operators with imaginary dimensions in the dual Euclidean three-dimensional conformal field theory. By making use of the dS/CFT correspondence we show that, besides t…
Necessary and sufficient conditions for large Nc equivalence between parent and daughter theories, for a wide class of orbifold projections of U(Nc) gauge theories, are just the natural requirements that the discrete symmetry used to define the projection not be spontaneously broken in the parent theory, and the discrete symmetry permuting equivalent gauge group factors not be spontaneously broken in the daughter theory. In this paper, we discuss the application of this result to Z_k projections of N=1 supersymmetric Yang-Mills theory in four dimensions, as well as various multi-flavor general…
We study a two dimensional dilaton gravity system, recently examined by Almheiri and Polchinski, which describes near extremal black holes, or more generally, nearly $AdS_2$ spacetimes. The asymptotic symmetries of $AdS_2$ are all the time reparametrizations of the boundary. These symmetries are spontaneously broken by the $AdS_2$ geometry and they are explicitly broken by the small deformation away from $AdS_2$. This pattern of spontaneous plus explicit symmetry breaking governs the gravitational backreaction of the system. It determines several gravitational properties such as the linear in …
We apply the methods of modern analytic bootstrap to the critical $O(N)$ model in a $1/N$ expansion. At infinite $N$ the model possesses higher spin symmetry which is weakly broken as we turn on $1/N$. By studying consistency conditions for the correlator of four fundamental fields we derive the CFT-data for all the (broken) currents to order $1/N$, and the CFT-data for the non-singlet currents to order $1/N^2$. To order $1/N$ our results are in perfect agreement with those in the literature. To order $1/N^2$ we reproduce known results for anomalous dimensions and obtain a variety of new resul…
We study three dimensional conformal field theories described by U(N) Chern-Simons theory at level k coupled to massless fermions in the fundamental representation. By solving a Schwinger-Dyson equation in lightcone gauge, we compute the exact planar free energy of the theory at finite temperature on R^2 as a function of the 't Hooft coupling lambda=N/k. Employing a dimensional reduction regularization scheme, we find that the free energy vanishes at |lambda|=1; the conformal theory does not exist for |lambda|>1. We analyze the operator spectrum via the anomalous conservation relation for high…
The cosmological Slavnov-Taylor (ST) identity of the Einstein-Hilbert action coupled to a single inflaton field is obtained from the Becchi-Rouet-Stora-Tyutin (BRST) symmetry associated with diffeomorphism invariance in the Arnowitt-Deser-Misner (ADM) formalism. The consistency conditions between the correlators of the scalar and tensor modes in the squeezed limit are then derived from the ST identity, together with the softly broken conformal symmetry. Maldacena's original relations connecting the 2- and 3-point correlators at horizon crossing are recovered, as well as the next-to-leading cor…
We study the imprints of massive particles with spin on cosmological correlators. Using the framework of the effective field theory of inflation, we classify the couplings of these particles to the Goldstone boson of broken time translations and the graviton. We show that it is possible to generate observable non-Gaussianity within the regime of validity of the effective theory, as long as the masses of the particles are close to the Hubble scale and their interactions break the approximate conformal symmetry of the inflationary background. We derive explicit shape functions for the scalar and…
In this paper, we introduce an $\mathcal{N}=1$ supersymmetric SYK model with $SO(q)$ global symmetry. We study the large $N$ expansion of the bi-local collective action of our model. At strong coupling limit, this model exhibits a super-reparametrization symmetry, and the $SO(q)$ global symmetry is enhanced to a $\widehat{SO}(q)$ local symmetry. The corresponding symmetry algebra is the semi-direct product of the super-Virasoro and the super-Kac-Moody algebras. These emergent symmetries are spontaneously and explicitly broken, which leads to a low energy effective action: super-Schwarzian acti…
In contrast to massless spinning particles, scalars are not heavily constrained by unitarity and locality. Off-shell, no gauge symmetries are required to write down manifestly local theories, while on-shell consistent factorisation is trivial. Instead a useful classification scheme for scalars is based on the symmetries they can non-linearly realise. Motivated by the breaking of Lorentz boosts in cosmology, in this paper we classify the possible symmetries of a shift-symmetric scalar that is assumed to non-linearly realise Lorentz boosts as, for example, in the EFT of inflation. Our classifica…
The dynamics of a dense relativistic quantum fluid out of thermodynamic equilibrium is studied in the framework of the Phi^4 scalar field theory in the large N limit. The time evolution of a particle distribution in momentum space (the tsunami) is computed. The effective mass felt by the particles in such a high density medium equals the tree level mass plus the expectation value of the squared field. The case of negative tree level squared mass is particularly interesting. In such case dynamical symmetry restoration as well as dynamical symmetry breaking can happen. Furthermore, the symmetry …
