arXiv subjects

Valentina Prilepina

Publications and source records attributed to Valentina Prilepina.

15 recordsLinked to original sources

arXiv2025

Mixed five-point correlators in the 3d Ising model

We study five-point correlators of the $σ$, $ε$, and $ε'$ operators in the critical 3d Ising model. We consider the $σ\times σ$ and $σ\times ε$ operator product expansions (OPEs) and truncate them by including a finite set of exchanged operators. We approximate the truncated operators by the corresponding contributions in appropriate disconnected five-point correlators. We compute a number of OPE coefficients that were previously unknown and show that these are consistent with predictions obtained using the fuzzy sphere regularization of the critical 3d Ising model.

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arXiv2025

Improving the five-point bootstrap

We present a new algorithm for the numerical evaluation of five-point conformal blocks in $d$-dimensions, greatly improving the efficiency of their computation. To do this we use an appropriate ansatz for the blocks as a series expansion in radial coordinates, derive a set of recursion relations for the unknown coefficients in the ansatz, and evaluate the series using a Padé approximant to accelerate its convergence. We then study the $\langleσσεσσ\rangle$ correlator in the 3d critical Ising model by truncating the operator product expansion (OPE) and only including operators with conformal dimension below a cutoff $Δ\leqslant Δ_{\rm cutoff}$. We approximate the contributions of the operators above the cutoff by the corresponding contributions in a suitable disconnected five-point correlator. Using this approach, we compute a number of OPE coefficients with greater accuracy than previous methods.

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arXiv2025

Conformal Bootstrap Equations from the Embedding Space Operator Product Expansion

We describe how to implement the conformal bootstrap program in the context of the embedding space OPE formalism introduced in previous work. To take maximal advantage of the known properties of the scalar conformal blocks for symmetric-traceless exchange, we construct tensorial generalizations of the three-point and four-point scalar conformal blocks that have many nice properties. Further, we present a special basis of tensor structures for three-point correlation functions endowed with the remarkable simplifying property that it does not mix under permutations of the external quasi-primary operators. We find that in this approach, we can write the $M$-point conformal bootstrap equations explicitly in terms of the standard position space cross-ratios without the need to project back to position space, thus effectively deriving all conformal bootstrap equations directly from the embedding space. Finally, we lay out an algorithm for generating the conformal bootstrap equations in this formalism. Collectively, the tensorial generalizations, the new basis of tensor structures, as well as the procedure for deriving the conformal bootstrap equations lead to four-point bootstrap equations for quasi-primary operators in arbitrary Lorentz representations expressed as linear combinations of the standard scalar conformal blocks for spin-$\ell$ exchange, with finite $\ell$-independent terms. Moreover, the OPE coefficients in these equations conveniently feature trivial symmetry properties. The only inputs necessary are the relevant projection operators and tensor structures, which are all fixed by group theory. To illustrate the procedure, we present one nontrivial example involving scalars $S$ and vectors $V$, namely $\left\langle SSSV\right\rangle$.

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arXiv2024

The five-point bootstrap

We study five-point correlation functions of scalar operators in d-dimensional conformal field theories. We develop a new approach to computing the five-point conformal blocks for exchanged primary operators of arbitrary spin by introducing a generalization of radial coordinates, using an appropriate ansatz, and perturbatively solving two quadratic Casimir differential equations. We then study five-point correlators $\langle σσεσσ\rangle$ in the critical 3d Ising model. We truncate the operator product expansions (OPEs) in the correlator by including a finite number of primary operators with conformal dimension below a cutoff $Δ\leqslant Δ_{\rm cutoff}$. We then compute several OPE coefficients involving $ε$ and two spinning operators by demanding that the truncated correlator approximately satisfies the crossing relation.

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arXiv2022

Thermal Stress Tensor Correlators, OPE and Holography

In strongly coupled conformal field theories with a large central charge important light degrees of freedom are the stress tensor and its composites, multi-stress tensors. We consider the OPE expansion of two-point functions of the stress tensor in thermal and heavy states and focus on the contributions from the stress tensor and double-stress tensors in four spacetime dimensions. We compare the results to the holographic finite temperature two-point functions and read off conformal data beyond the leading order in the large central charge expansion. In particular, we compute corrections to the OPE coefficients which determine the near-lightcone behavior of the correlators. We also compute the anomalous dimensions of the double-stress tensor operators.

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arXiv2022

Recursion relations for 5-point conformal blocks

We consider 5-point functions in conformal field theories in d > 2 dimensions. Using weight-shifting operators, we derive recursion relations which allow for the computation of arbitrary conformal blocks appearing in 5-point functions of scalar operators, reducing them to a linear combination of blocks with scalars exchanged. We additionally derive recursion relations for the conformal blocks which appear when one of the external operators in the 5-point function has spin 1 or 2. Our results allow us to formulate positivity constraints using 5-point functions which describe the expectation value of the energy operator in bilocal states created by two scalars.

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arXiv2020

Conformal Conserved Currents in Embedding Space

We study conformal conserved currents in arbitrary irreducible representations of the Lorentz group using the embedding space formalism. With the help of the operator product expansion, we first show that conservation conditions can be fully investigated by considering only two- and three-point correlation functions. We then find an explicitly conformally-covariant differential operator in embedding space that implements conservation based on the standard position space operator product expansion differential operator $\partial_μ$, although the latter does not uplift to embedding space covariantly. The differential operator in embedding space that imposes conservation is the same differential operator $\mathcal{D}_{ijA}$ used in the operator product expansion in embedding space. We provide several examples including conserved currents in irreducible representations that are not symmetric and traceless. With an eye on four-point conformal bootstrap equations for four conserved vector currents $\langle JJJJ\rangle$ and four energy-momentum tensors $\langle TTTT\rangle$, we mostly focus on conservation conditions for $\langle JJ\mathcal{O}\rangle$ and $\langle TT\mathcal{O}\rangle$. Finally, we reproduce and extend the consequences of conformal Ward identities at coincident points by determining three-point coefficients in terms of charges.

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arXiv2020

Efficient Rules for All Conformal Blocks

We formulate a set of general rules for computing $d$-dimensional four-point global conformal blocks of operators in arbitrary Lorentz representations in the context of the embedding space operator product expansion formalism arXiv:1905.00434. With these rules, the procedure for determining any conformal block of interest is reduced to (1) identifying the relevant projection operators and tensor structures and (2) applying the conformal rules to obtain the blocks. To facilitate the bookkeeping of contributing terms, we introduce a convenient diagrammatic notation. We present several concrete examples to illustrate the general procedure as well as to demonstrate and test the explicit application of the rules. In particular, we consider four-point functions involving scalars $S$ and some specific irreducible representations $R$, namely $\langle SSSS\rangle$, $\langle SSSR\rangle$, $\langle SRSR\rangle$ and $\langle SSRR\rangle$ (where, when allowed, $R$ is a vector or a fermion), and determine the corresponding blocks for all possible exchanged representations.

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arXiv2019

Conformal Four-Point Correlation Functions from the Operator Product Expansion

We show how to compute conformal blocks of operators in arbitrary Lorentz representations using the formalism described in arXiv:1905.00036 and arXiv:1905.00434, and present several explicit examples of blocks derived via this method. The procedure for obtaining the blocks has been reduced to (1) determining the relevant group theoretic structures and (2) applying appropriate predetermined substitution rules. The most transparent expressions for the blocks we find are expressed in terms of specific substitutions on the Gegenbauer polynomials. In our examples, we study operators which transform as scalars, symmetric tensors, two-index antisymmetric tensors, as well as mixed representations of the Lorentz group.

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arXiv2019

Conformal Three-Point Correlation Functions from the Operator Product Expansion

We show how to construct embedding space three-point functions for operators in arbitrary Lorentz representations by employing the formalism developed in arXiv:1905.00036 and arXiv:1905.00434. We study tensor structures that intertwine the operators with the derivatives in the OPE and examine properties of OPE coefficients under permutations of operators. Several examples are worked out in detail. We point out that the group theoretic objects used in this work can be applied directly to construct three-point functions without any reference to the OPE.

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arXiv2019

Conformal Two-Point Correlation Functions from the Operator Product Expansion

We compute the most general embedding space two-point function in arbitrary Lorentz representations in the context of the recently introduced formalism in arXiv:1905.00036 and arXiv:1905.00434. This work provides a first explicit application of this approach and furnishes a number of checks of the formalism. We project the general embedding space two-point function to position space and find a form consistent with conformal covariance. Several concrete examples are worked out in detail. We also derive constraints on the OPE coefficient matrices appearing in the two-point function, which allow us to impose unitarity conditions on the two-point function coefficients for operators in any Lorentz representations.

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arXiv2017

Weyl versus Conformal Invariance in Quantum Field Theory

We argue that conformal invariance in flat spacetime implies Weyl invariance in a general curved background metric for all unitary theories in spacetime dimensions $d \leq 10$. We also study possible curvature corrections to the Weyl transformations of operators, and show that these are absent for operators of sufficiently low dimensionality and spin. We find possible `anomalous' Weyl transformations proportional to the Weyl (Cotton) tensor for $d > 3$ ($d = 3$). The arguments are based on algebraic consistency conditions similar to the Wess-Zumino consistency conditions that classify possible local anomalies. The arguments can be straightforwardly extended to larger operator dimensions and higher $d$ with additional algebraic complexity.

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arXiv2017

Reconciling Large And Small-Scale Structure In Twin Higgs Models

We study extensions of the Twin Higgs model that solve the Hierarchy problem and simultaneously address problems of the large- and small-scale structures of the Universe. Besides naturally providing dark matter (DM) candidates as the lightest charged twin fermions, the twin sector contains a light photon and neutrinos, which can modify structure formation relative to the prediction from the $Λ$CDM paradigm. We focus on two scenarios. First, we study a Fraternal Twin Higgs model in which the spin-3/2 baryon $\hatΩ\sim(\hat{b}\hat{b}\hat{b})$ and the lepton twin tau $\hatτ$ contribute to the dominant and subcomponent dark matter densities. A non-decoupled scattering between the twin tau and twin neutrino arising from a gauged twin lepton number symmetry provides a drag force that damps the density inhomogeneity of a dark matter subcomponent. Next, we consider the possibility of having the twin hydrogen atom $\hat{H}$ as the dominant DM component. After recombination, a small fraction of the twin protons and leptons remains ionized during structure formation, and their scattering to twin neutrinos through a gauged U$(1)_{B-L}$ force provides the mechanism that damps the density inhomogeneity. Both scenarios realize the Partially Acoustic dark matter (PAcDM) scenario and explain the $σ_8$ discrepancy between the CMB and weak lensing results. Moreover, the self-scattering neutrino behaves as a dark fluid that enhances the size of the Hubble rate $H_0$ to accommodate the local measurement result while satisfying the CMB constraint. For the small-scale structure, the scattering of $\hatΩ$'s and $\hat{H}$'s through the twin photon exchange generates a self-interacting dark matter (SIDM) model that solves the mass deficit problem from dwarf galaxy to galaxy cluster scales.

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arXiv2016

Positive Energy Conditions in 4D Conformal Field Theory

We argue that all consistent 4D quantum field theories obey a spacetime-averaged weak energy inequality $\langle T^{00} \rangle \ge -C/L^4$, where $L$ is the size of the smearing region, and $C$ is a positive constant that depends on the theory. If this condition is violated, the theory has states that are indistinguishable from states of negative total energy by any local measurement, and we expect instabilities or other inconsistencies. We apply this condition to 4D conformal field theories, and find that it places constraints on the OPE coefficients of the theory. The constraints we find are weaker than the "conformal collider" constraints of Hofman and Maldacena. We speculate that there may be theories that violate the Hofman-Maldacena bounds, but satisfy our bounds. In 3D CFTs, the only constraint we find is equivalent to the positivity of 2-point function of the energy-momentum tensor, which follows from unitarity. Our calculations are performed using momentum-space Wightman functions, which are remarkably simple functions of momenta, and may be of interest in their own right.

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arXiv2014

Scale Invariance, Conformality, and Generalized Free Fields

This paper addresses the question of whether there are 4D Lorentz invariant unitary quantum field theories with scale invariance but not conformal invariance. An important loophole in the arguments of Luty-Polchinski-Rattazzi and Dymarsky-Komargodski-Schwimmer-Theisen is that trace of the energy-momentum tensor $T$ could be a generalized free field. In this paper we rule out this possibility. The key ingredient is the observation that a unitary theory with scale but not conformal invariance necessarily has a non-vanishing anomaly for global scale transformations. We show that this anomaly cannot be reproduced if $T$ is a generalized free field unless the theory also contains a dimension-2 scalar operator. In the special case where such an operator is present it can be used to redefine ("improve") the energy-momentum tensor, and we show that there is at least one energy-momentum tensor that is not a generalized free field. In addition, we emphasize that, in general, large momentum limits of correlation functions cannot be understood from the leading terms of the coordinate space OPE. This invalidates a recent argument by Farnsworth-Luty-Prilepina (FLP). Despite the invalidity of the general argument of FLP, some of the techniques turn out to be useful in the present context.

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