arXiv subjects

Dean Carmi

Publications and source records attributed to Dean Carmi.

At least 19 recordsLinked to original sources

arXiv2026

Aspects of Witten Diagrams for Holographic Defects

In this paper, we study the conformal block decomposition of Witten diagrams for $d$-dimensional holographic CFTs in the presence of a $p$-dimensional conformal defect. The holographic dual in this case contains a probe AdS$_{p+1}$ brane embedded inside AdS$_{d+1}$. In particular, we focus on contact, tree-level exchanges and some one-loop two-point Witten diagrams, which contribute to the two-point function of CFT bulk scalar operators. We also consider a tree-level exchange diagram for a three-point function involving one CFT bulk scalar operator and two scalar operators localized on the defect. Employing the split representation of AdS propagators, adapted to the probe brane setup, we perform the direct channel conformal block decompositions of these diagrams. In the case of tree-level diagrams, we obtain explicit expressions for the OPE coefficients in the direct channel decompositions. For two-point tree-level exchange diagrams, we derive recursion relations for the coefficients in the crossed-channel block expansions and compute the seed coefficients which serve as inputs for these relations. Our explicit results for the block decomposition coefficients for tree-level Witten diagrams are potentially useful for further developing the analytic functional approach to bootstrapping two-point functions of bulk operators in general defect CFTs. We also study the crossing kernel, which encodes the bulk channel partial wave expansion of a defect channel partial wave. Using the bulk channel Lorentzian inversion formula for defect CFTs, we derive closed form expressions for this defect-to-bulk channel crossing kernel for zero-dimensional defects in $d=2,4$ dimensions and surface defects in $d=4,6$ dimensions.

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arXiv2026

Closing the loop on $\Phi^4$ in AdS$_3$

We compute the one-loop correction to the CFT data of all double-trace operators $[\phi\phi]_{n,\ell}$ for a $\Phi^4$ theory in AdS$_3$, for arbitrary values of $n$, $\ell$, and of the scaling dimension $\Delta_\phi>1$. Working in the spectral representation, the $t$-channel one-loop bubble diagram is reduced to a product of spectral integrals dressed by the conformal $6j$ symbol. Both the spectral integrals and the subsequent sums over residues are performed analytically, yielding finite closed-form expressions for the anomalous dimensions in terms of higher hypergeometric functions. We discuss the structure of the results, including their large-spin and high-energy behaviors, and show that the anomalous dimensions are completely monotonic in spin.

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arXiv2025

Conformal dispersion relation for mixed correlators

Dispersion relations are nonperturbative formulas that relate the ultraviolet and infrared behavior of an observable with wide-ranging applications applications in linear response theory, quantum field theory scattering amplitudes, and conformal correlators. We derive a position-space dispersion relation for scalar four-point mixed correlation functions in an arbitrary conformal field theory. This formula expresses the correlator in terms of its integrated double discontinuity times a kinematic kernel. The kernel is analytically computed, and expressed in a remarkably simple form as a two-variable Appell function. The dispersion kernel is found by solving a coupled partial differential equation that the kernel obeys. Numerical checks of the dispersion relation are successfully performed for generalized free field correlators. Finally, we show that our position-space dispersion relation is equivalent to a Cauchy-type dispersion relation of the Mellin amplitude of the correlator.

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arXiv2024

1d Conformal Field Theory and Dispersion Relations

We study conformal field theory in $d=1$ space-time dimensions. We derive a dispersion relation for the 4-point correlation function of identical bosons and fermions, in terms of the double discontinuity. This extends the conformal dispersion relation of arXiv:1910.12123, which holds for CFTs in dimensions $d\geq 2$, to the case of $d=1$. The dispersion relation is obtained by combining the Lorentzian inversion formula with the operator product expansion of the 4-point correlator. We perform checks of the dispersion relation using correlators of generalised free fields and derive an integral relation between the kernel of the dispersion relation and that of the Lorentzian inversion formula. Finally, for $1$-$d$ holographic conformal theories, we analytically compute scalar Witten diagrams in $AdS_2$ at tree-level and $1$-loop.

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arXiv2024

Loops in AdS: From the Spectral Representation to Position Space III

We study loop amplitudes in anti de-Sitter space via the spectral representation. We consider loops of spinning fields and in particular gauge fields, and derive various identities connecting different families of loop diagrams, at different number of loops, different spins, different masses. Such identities are useful for the computation of Witten diagrams. Considering the theory of large-$N_f$ conformal scalar QED defined on AdS space, we derive an analytic expression for the exact 4-point correlation function at sub-leading order in $\frac{1}{N_f}$. Additionally, we derive analytic expressions for bulk 2-point functions and boundary 4-point functions for various families of diagrams, which we denote as ``blob diagrams''. Finally we study 4-point ladder diagrams with spinning fields, and we derive integral expressions for the spectral representation of a $k$-loop ladder diagram.

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arXiv2023

Scalar QED in AdS

We consider scalar QED with $N_f$ flavors in AdS$_D$. For $D<4$ the theory is strongly-coupled in the IR. We use the spin 1 spectral representation to compute and efficiently resum the bubble diagram in AdS, in order to obtain the exact propagator of the photon at large $N_f$. We then apply this result to compute the boundary four-point function of the charged operators at leading order in $1/N_f$ and exactly in the coupling, both in the Coulomb and in the Higgs phase. In the first case a conserved current is exchanged in the four-point function, while in the second case the current is absent and there is a pattern of double-trace scaling dimension analogous to a resonance in flat space. We also consider the BCFT data associated to the critical point with bulk conformal symmetry separating the two phases. Both in ordinary perturbation theory and at large $N_f$, in integer dimension $D= 3$ an IR divergence breaks the conformal symmetry on the boundary by inducing a boundary RG flow in a current-current operator.

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arXiv2021

Loops in AdS: From the Spectral Representation to Position Space II

We continue the study of AdS loop amplitudes in the spectral representation and in position space. We compute the finite coupling 4-point function in position space for the large-$N$ conformal Gross Neveu model on $AdS_3$. The resummation of loop bubble diagrams gives a result proportional to a tree-level contact diagram. We show that certain families of fermionic Witten diagrams can be easily computed from their companion scalar diagrams. Thus, many of the results and identities of [1] are extended to the case of external fermions. We derive a spectral representation for ladder diagrams in AdS. Finally, we compute various bulk 2-point correlators, extending the results of [1].

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arXiv2021

Loops in AdS: From the Spectral Representation to Position Space

We compute a family of scalar loop diagrams in $AdS$. We use the spectral representation to derive various bulk vertex/propagator identities, and these identities enable to reduce certain loop bubble diagrams to lower loop diagrams, and often to tree-level exchange or contact diagrams. An important example is the computation of the finite coupling 4-point function of the large-$N$ conformal $O(N)$ model on $AdS_3$. Remarkably, the re-summation of bubble diagrams is equal to a tree-level contact diagram: the $\bar{D}_{1,1,\frac{3}{2},\frac{3}{2}} (z,\bar z)$ function. Another example is a scalar with $ϕ^4$ or $ϕ^3$ coupling in $AdS_3$: we compute various 4-point (and higher point) loop bubble diagrams with alternating integer and half-integer scaling dimensions in terms of a finite sum of contact diagrams and tree-level exchange diagrams. The 4-point function with external scaling dimensions differences obeying $Δ_{12}=0$ and $Δ_{34}=1$ enjoys significant simplicity which enables us to compute in quite generality. For integer or half-integer scaling dimensions, we show that the $M$-loop bubble diagram can be written in terms of Lerch transcendent functions of the cross-ratios $z$ and $\bar z$. Finally, we compute 2-point bulk bubble diagrams with endpoints in the bulk, and the result can be written in terms of Lerch transcendent functions of the AdS chordal distance. We show that the similarity of the latter two computations is not a coincidence, but arises from a vertex identity between the bulk 2-point function and the double-discontinuity of the boundary 4-point function.

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arXiv2021

Applications of dispersive sum rules: $ε$-expansion and holography

We use Mellin space dispersion relations together with Polyakov conditions to derive a family of sum rules for Conformal Field Theories (CFTs). The defining property of these sum rules is suppression of the contribution of the double twist operators. Firstly, we apply these sum rules to the Wilson-Fisher model in $d=4-ε$ dimensions. We re-derive many of the known results to order $ε^4$ and we make new predictions. No assumption of analyticity down to spin $0$ was made. Secondly, we study holographic CFTs. We use dispersive sum rules to obtain tree-level and one-loop anomalous dimensions. Finally, we briefly discuss the contribution of heavy operators to the sum rules in UV complete holographic theories.

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arXiv2020

A Conformal Dispersion Relation: Correlations from Absorption

We introduce the analog of Kramers-Kronig dispersion relations for correlators of four scalar operators in an arbitrary conformal field theory. The correlator is expressed as an integral over its 'absorptive part', defined as a double discontinuity, times a theory-independent kernel which we compute explicitly. The kernel is found by resumming the data obtained by the Lorentzian inversion formula. For scalars of equal scaling dimensions, it is a remarkably simple function (elliptic integral function) of two pairs of cross-ratios. We perform various checks of the dispersion relation (generalized free fields, holographic theories at tree-level, 3D Ising model), and get perfect matching. Finally, we derive an integral relation that relates the 'inverted' conformal block with the ordinary conformal block.

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arXiv2019

Comments on Holographic Complexity

We study two recent conjectures for holographic complexity: the complexity=action conjecture and the complexity=volume conjecture. In particular, we examine the structure of the UV divergences appearing in these quantities, and show that the coefficients can be written as local integrals of geometric quantities in the boundary. We also consider extending these conjectures to evaluate the complexity of the mixed state produced by reducing the pure global state to a specific subregion of the boundary time slice. The UV divergences in this subregion complexity have a similar geometric structure, but there are also new divergences associated with the geometry of the surface enclosing the boundary region of interest. We discuss possible implications arising from the geometric nature of these UV divergences.

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arXiv2019

A Study of Quantum Field Theories in AdS at Finite Coupling

We study the $O(N)$ and Gross-Neveu models at large $N$ on AdS$_{d+1}$ background. Thanks to the isometries of AdS, the observables in these theories are constrained by the SO$(d,2)$ conformal group even in the presence of mass deformations, as was discussed by Callan and Wilczek, and provide an interesting two-parameter family of quantities which interpolate between the S-matrices in flat space and the correlators in CFT with a boundary. For the actual computation, we judiciously use the spectral representation to resum loop diagrams in the bulk. After the resummation, the AdS $4$-particle scattering amplitude is given in terms of a single unknown function of the spectral parameter. We then "bootstrap" the unknown function by requiring the absence of double-trace operators in the boundary OPE. Our results are at leading nontrivial order in $\frac{1}{N}$, and include the full dependence on the quartic coupling, the mass parameters, and the AdS radius. In the bosonic $O(N)$ model we study both the massive phase and the symmetry-breaking phase, which exists even in AdS$_2$ evading Coleman's theorem, and identify the AdS analogue of a resonance in flat space. We then propose that symmetry breaking in AdS implies the existence of a conformal manifold in the boundary conformal theory. We also provide evidence for the existence of a critical point with bulk conformal symmetry, matching existing results and finding new ones for the conformal boundary conditions of the critical theories. For the Gross-Neveu model we find a bound state, which interpolates between the familiar bound state in flat space and the displacement operator at the critical point.

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arXiv2017

More on Holographic Volumes, Entanglement, and Complexity

Motivated by the holographic prescriptions for computing entanglement entropy and complexity, we study the properties of volumes/areas of bulk surfaces. We obtain a simple formula for the shape dependence of holographic entanglement entropy in terms of a certain integral over the entangling surface. This easily generalizes to any bulk codimension-$p$ extremal surface. We study additional properties of bulk codimension-$p$ extremal surfaces corresponding to strip/plane "entangling surfaces" in various geometries. We compute universal terms for codim-one volumes (conjectured to be dual to holographic subregion complexity) arising from performing relevant deformations. Finally, we describe several interesting bulk surface constructions which are presumably related to holographic complexity.

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arXiv2017

On the Time Dependence of Holographic Complexity

We evaluate the full time dependence of holographic complexity in various eternal black hole backgrounds using both the complexity=action (CA) and the complexity=volume (CV) conjectures. We conclude using the CV conjecture that the rate of change of complexity is a monotonically increasing function of time, which saturates from below to a positive constant in the late time limit. Using the CA conjecture for uncharged black holes, the holographic complexity remains constant for an initial period, then briefly decreases but quickly begins to increase. As observed previously, at late times, the rate of growth of the complexity approaches a constant, which may be associated with Lloyd's bound on the rate of computation. However, we find that this late time limit is approached from above, thus violating the bound. Adding a charge to the eternal black holes washes out the early time behaviour, i.e., complexity immediately begins increasing with sufficient charge, but the late time behaviour is essentially the same as in the neutral case. We also evaluate the complexity of formation for charged black holes and find that it is divergent for extremal black holes, implying that the states at finite chemical potential and zero temperature are infinitely more complex than their finite temperature counterparts.

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arXiv2016

On Volumes of Subregions in Holography and Complexity

The volume of the region inside the bulk Ryu-Takayanagi surface is a codimension-one object, and a natural generalization of holographic complexity to the case of subregions in the boundary QFT. We focus on time-independent geometries, and study the properties of this volume in various circumstances. We derive a formula for computing the volume for a strip entangling surface and a general asymptotically AdS bulk geometry. For an AdS black hole geometry, the volume exhibits non-monotonic behaviour as a function of the size of the entangling region (unlike the behaviour of the entanglement entropy in this setup, which is monotonic). For setups in which the holographic entanglement entropy exhibits transitions in the bulk, such as global AdS black hole, geometries dual to confining theories and disjoint entangling surfaces, the corresponding volume exhibits a discontinuous finite jump at the transition point (and so do the volumes of the corresponding entanglement wedges). We compute this volume discontinuity in several examples. Lastly, we compute the codim-zero volume and the bulk action of the entanglement wedge for the case of a sphere entangling surface and pure AdS geometry.

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arXiv2015

On the Shape Dependence of Entanglement Entropy

We study the shape dependence of entanglement entropy (EE) by deforming symmetric entangling surfaces. We show that entangling surfaces with a rotational or translational symmetry extremize (locally) the EE with respect to shape deformations that break some of the symmetry (i.e. the 1st order correction vanishes). This result applies to EE and Renyi entropy for any QFT in any dimension. Using Solodukhin's formula in $4d$ and holography in any $d$, we calculate the 2nd order correction to the universal EE for CFTs and simple symmetric entangling surfaces. In all cases we find that the 2nd order correction is positive, and thus the corresponding symmetric entangling surface is a local minimum. Some of the results are extended to free massive fields and to 4d Renyi entropy.

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arXiv2015

TeV Scale Strings and Scattering Amplitudes at the LHC

We study aspects of TeV string scale models of intersecting D-branes. The gauge bosons arise from strings ending on stacks of D-branes, whereas chiral matter arises from strings stretched between intersecting D-branes. Our focus is on scattering amplitudes (at tree-level), Regge states (string excitations), and collider phenomenology. Achieving a low string scale is possible in models of Large extra dimensions. At the LHC, a low enough string scale implies that cross sections will deviate from their standard model predictions. Moreover, Regge states as well as Kaluza-Klein states and winding states may be produced. In a large class of intersecting D-brane models, the quark-gluon amplitudes with at most 2 quarks turn out to be independent of the geometry of the extra dimensions. Therefore these type of amplitudes, which we call "universal amplitudes", are model independent. The universal amplitudes involve exchanges of Regge states only, whereas amplitudes with more then 2 quarks also involve exchanges of KK and winding states. The main computational part of this work is concerned with suggesting methods to calculate the decay widths of the Regge states, and with the formalism for treating amplitudes containing exchanges of higher spin particles.

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arXiv2015

Renormalization group flow of entanglement entropy on spheres

We explore entanglement entropy of a cap-like region for a generic quantum field theory residing in the Bunch-Davies vacuum on de Sitter space. Entanglement entropy in our setup is identical with the thermal entropy in the static patch of de Sitter, and we derive a simple relation between the vacuum expectation value of the energy-momentum tensor trace and the RG flow of entanglement entropy. In particular, renormalization of the cosmological constant and logarithmic divergence of the entanglement entropy are interrelated in our setup. We confirm our findings by recovering known universal contributions for a free field theory deformed by a mass operator as well as obtain correct universal behaviour at the fixed points. Simple examples of entanglement entropy flows are elaborated in $d=2,3,4$. In three dimensions we find that while the renormalized entanglement entropy is stationary at the fixed points, it is not monotonic. We provide a computational evidence that the universal `area law' for a conformally coupled scalar is different from the known result in the literature, and argue that this difference survives in the limit of flat space. Finally, we carry out the spectral decomposition of entanglement entropy flow and discuss its application to the F-theorem.

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