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Agnese Bissi

Publications and source records attributed to Agnese Bissi.

At least 37 records · Page 2Linked to original sources
arXiv2019

Dispersion Relation for CFT Four-Point Functions

We present a dispersion relation in conformal field theory which expresses the four point function as an integral over its single discontinuity. Exploiting the analytic properties of the OPE and crossing symmetry of the correlator, we show that in perturbative settings the correlator depends only on the spectrum of the theory, as well as the OPE coefficients of certain low twist operators, and can be reconstructed unambiguously. In contrast to the Lorentzian inversion formula, the validity of the dispersion relation does not assume Regge behavior and is not restricted to the exchange of spinning operators. As an application, the correlator $\langle ϕϕϕϕ\rangle$ in $ϕ^4$ theory at the Wilson-Fisher fixed point is computed in closed form to order $ε^2$ in the $ε$ expansion.

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arXiv2019

Genus-One String Amplitudes from Conformal Field Theory

We explore and exploit the relation between non-planar correlators in ${\cal N}=4$ super-Yang-Mills, and higher-genus closed string amplitudes in type IIB string theory. By conformal field theory techniques we construct the genus-one, four-point string amplitude in AdS$_5\times S^5$ in the low-energy expansion, dual to an ${\cal N}=4$ super-Yang-Mills correlator in the 't Hooft limit at order $1/c^2$ in a strong coupling expansion. In the flat space limit, this maps onto the genus-one, four-point scattering amplitude for type II closed strings in ten dimensions. Using this approach we reproduce several results obtained via string perturbation theory. We also demonstrate a novel mechanism to fix subleading terms in the flat space limit of AdS amplitudes by using string/M-theory.

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arXiv2018

The Analytic Bootstrap for Large $N$ Chern-Simons Vector Models

Three-dimensional Chern-Simons vector models display an approximate higher spin symmetry in the large $N$ limit. Their single-trace operators consist of a tower of weakly broken currents, as well as a scalar $σ$ of approximate twist $1$ or $2$. We study the consequences of crossing symmetry for the four-point correlator of $σ$ in a $1/N$ expansion, using analytic bootstrap techniques. To order $1/N$ we show that crossing symmetry fixes the contribution from the tower of currents, providing an alternative derivation of well-known results by Maldacena and Zhiboedov. When $σ$ has twist $1$ its OPE receives a contribution from the exchange of $σ$ itself with an arbitrary coefficient, due to the existence of a marginal sextic coupling. We develop the machinery to determine the corrections to the OPE data of double-trace operators due to this, and to similar exchanges. This in turns allows us to fix completely the correlator up to three known truncated solutions to crossing. We then proceed to study the problem to order $1/N^2$. We find that crossing implies the appearance of odd-twist double-trace operators, and calculate their OPE coefficients in a large spin expansion. Also, surprisingly, crossing at order $1/N^2$, implies non-trivial $O(1/N)$ anomalous dimensions for even-twist double-trace operators, even though such contributions do not appear in the four-point function at order $1/N$ (in the case where there is no scalar exchange). We argue that this phenomenon arises due to operator mixing. Finally, we analyse the bosonic vector model with a sextic coupling without gauge interactions, and determine the order $1/N^2$ corrections to the dimensions of twist-$2$ double-trace operators.

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arXiv2018

Holographic Reconstruction of AdS Exchanges from Crossing Symmetry

Motivated by AdS/CFT, we address the following outstanding question in large $N$ conformal field theory: given the appearance of a single-trace operator in the ${\cal O}\times{\cal O}$ OPE of a scalar primary ${\cal O}$, what is its total contribution to the vacuum four-point function $\langle {\cal O}{\cal O}{\cal O}{\cal O}\rangle$ as dictated by crossing symmetry? We solve this problem in 4d conformal field theories at leading order in $1/N$. Viewed holographically, this provides a field theory reconstruction of crossing-symmetric, four-point exchange amplitudes in AdS$_5$. Our solution takes the form of a resummation of the large spin solution to the crossing equations, supplemented by corrections at finite spin, required by crossing. The method can be applied to the exchange of operators of arbitrary twist $τ$ and spin $s$, although it vastly simplifies for even-integer twist, where we give explicit results. The output is the set of OPE data for the exchange of all double-trace operators $[{\cal O}{\cal O}]_{n,\ell}$. We find that the double-trace anomalous dimensions $γ_{n,\ell}$ are negative, monotonic and convex functions of $\ell$, for all $n$ and all $\ell>s$. This constitutes a holographic signature of bulk causality and classical dynamics of even-spin fields. We also find that the "derivative relation" between double-trace anomalous dimensions and OPE coefficients does not hold in general, and derive the explicit form of the deviation in several cases. Finally, we study large $n$ limits of $γ_{n,\ell}$, relevant for the Regge and bulk-point regimes.

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arXiv2017

Loop Corrections to Supergravity on $AdS_5 \times S^5$

We consider the four-point correlator of the stress-energy tensor multiplet in ${\cal N}=4$ SYM. In the planar limit and at large 't Hooft coupling such correlator is given by the corresponding holographic correlation function in IIB supergravity on $AdS_5 \times S^5$. We consider subleading corrections in the number of colours, i.e. order $1/N^4$, at large 't Hooft coupling. This corresponds to loop corrections to the supergravity result. Consistency conditions, most notably crossing symmetry, constrain the form of such corrections and lead to a complete determination of the spectrum of leading twist intermediate operators.

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arXiv2016

Unitarity and positivity constraints for CFT at large central charge

We consider the four-point correlator of the stress tensor multiplet in ${\cal N}=4$ SYM in the limit of large central charge $c \sim N^2$. For finite values of $g^2N$ single-trace intermediate operators arise at order $1/c$ and this leads to specific poles in the Mellin representation of the correlator. The sign of the residue at these poles is fixed by unitarity. We consider solutions consistent with crossing symmetry and this pole structure. We show that in a certain regime all solutions result in a negative contribution to the anomalous dimension of twist four operators. The reason behind this is a positivity property of Mack polynomials that leads to a positivity condition for the Mellin amplitude. This positivity condition can also be proven by assuming the correct Regge behaviour for the Mellin amplitude. For large $g^2N$ we recover a tower of solutions in one to one correspondence with local interactions in a effective field theory in the $AdS$ bulk, with the appropriate suppression factors, and with definite overall signs. These signs agree with the signs that would follow from causality constraints on the effective field theory. The positivity constraints arising from CFT for the Mellin amplitude take a very similar form to the causality constraint for the forward limit of the S-matrix.

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arXiv2016

Crossing symmetry and Higher spin towers

We consider higher spin operators in weakly coupled gauge conformal field theories. Crossing symmetry of mixed scalar correlators relates different higher spin towers and we study the consequences for the spectrum and structure constants of higher spin operators of different twists. Constraints are obtained to all loops in perturbation theory. The large spin contributions to the structure constants can be resummed into a theory-dependent prefactor times a universal factor, whose structure of poles agrees with the one that would be obtained from a Witten diagram supergravity computation, although only crossing symmetry is assumed. Finally, our results provide an all loop expression for the double null limit of mixed correlators, which is in perfect agreement with the correlator/Wilson loop correspondence.

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arXiv2016

Revisiting N=4 superconformal blocks

We study four-point correlation functions of four generic half-BPS supermultiplets of N=4 SCFT in four dimensions. We use the two-particle Casimir of four-dimensional superconformal algebra to derive superconformal blocks which contribute to the partial wave expansion of such correlators. The derived blocks are defined on analytic superspace and allow us in principle to find any component of the four-point correlator. The lowest component of the result agrees with the superconformal blocks found by Dolan and Osborn.

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arXiv2016

Large spin systematics in CFT

Using conformal field theory (CFT) arguments we derive an infinite number of constraints on the large spin expansion of the anomalous dimensions and structure constants of higher spin operators. These arguments rely only on analiticity, unitarity, crossing-symmetry and the structure of the conformal partial wave expansion. We obtain results for both, perturbative CFT to all order in the perturbation parameter, as well as non-perturbatively. For the case of conformal gauge theories this provides a proof of the reciprocity principle to all orders in perturbation theory and provides a new "reciprocity" principle for structure constants. We argue that these results extend also to non-conformal theories.

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arXiv2015

Lessons from crossing symmetry at large N

We consider the four-point correlator of the stress tensor multiplet in N=4 SYM. We construct all solutions consistent with crossing symmetry in the limit of large central charge c ~ N^2 and large g^2 N. While we find an infinite tower of solutions, we argue most of them are suppressed by an extra scale Δ_{gap} and are consistent with the upper bounds for the scaling dimension of unprotected operators observed in the numerical superconformal bootstrap at large central charge. These solutions organize as a double expansion in 1/c and 1/Δ_{gap}. Our solutions are valid to leading order in 1/c and to all orders in 1/Δ_{gap} and reproduce, in particular, instanton corrections previously found. Furthermore, we find a connection between such upper bounds and positivity constraints arising from causality in flat space. Finally, we show that certain relations derived from causality constraints for scattering in AdS follow from crossing symmetry.

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arXiv2014

Generalized bootstrap equations for N=4 SCFT

We study the consistency of four-point functions of half-BPS chiral primary operators of weight p in four-dimensional N=4 superconformal field theories. The resulting conformal bootstrap equations impose non-trivial bounds for the scaling dimension of unprotected local operators transforming in various representations of the R-symmetry group. These bounds generalize recent bounds for operators in the singlet representation, arising from consistency of the four-point function of the stress-energy tensor multiplet.

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arXiv2013

Modular interpolating functions for N=4 SYM

We construct interpolating functions fully compatible with S-duality. We then consider the problem of resumming perturbative expansions for anomalous dimensions of low twist non-protected operators in N=4 super Yang-Mills theory. When the rank of the gauge group is small, the interpolations suggest that anomalous dimensions of leading twist operators take their maximum value at the point $τ=\exp(iπ/3)$. For fixed spin and large enough rank, there is a level-crossing region, where the anomalous dimension of the leading twist operator reaches its maximum and then bounces back.

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arXiv2013

The superconformal bootstrap for structure constants

We report on non-perturbative bounds for structure constants on N=4 SYM. Such bounds are obtained by applying the conformal bootstrap recently extended to superconformal theories. We compare our results with interpolating functions suitably restricted by the S-duality of the theory. Within numerical errors, these interpolations support the conjecture that the bounds found in this paper are saturated at duality invariant values of the coupling. This extends recent conjectures for the anomalous dimension of leading twist operators.

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arXiv2013

Higher-spin correlators

We analyze the properly normalized three-point correlator of two protected scalar operators and one higher spin twist-two operator in N=4 super Yang-Mills, in the limit of large spin j. The relevant structure constant can be extracted from the OPE of the four-point correlator of protected scalar operators. We show that crossing symmetry of the four point correlator plus a judicious guess for the perturbative structure of the three-point correlator, allow to make a prediction for the structure constant at all loops in perturbation theory, up to terms that remain finite as the spin becomes large. Furthermore, the expression for the structure constant allows to propose an expression for the all loops four-point correlator G(u,v), in the limit u,v -> 0. Our predictions are in perfect agreement with the large j expansion of results available in the literature.

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arXiv2013

On Three-point Functions in the AdS_4/CFT_3 Correspondence

We calculate planar, tree-level, non-extremal three-point functions of operators belonging to the SU(2) x SU(2) sector of ABJM theory. First, we generalize the determinant representation, found by Foda for the three-point functions of the SU(2) sector of N=4 SYM, to the present case and find that the ABJM result up to normalization factors factorizes into a product of two N=4 SYM correlation functions. Secondly, we treat the case where two operators are heavy and one is light and BPS, using a coherent state description of the heavy ones. We show that when normalized by the three-point function of three BPS operators the heavy-heavy-light correlation function agrees, in the Frolov-Tseytlin limit, with its string theory counterpart which we calculate holographically.

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arXiv2013

The SO(6) Scalar Product and Three-Point Functions from Integrability

In 1012.2475 Escobedo, Gromov, Sever and Vieira suggested a formula for an SU(2) three-point correlation function at weak coupling based on integrability techniques. We generalize it to the SO(6) sector, thus including all possible single-trace scalar operators in $\mathcal{N}=4$ super Yang-Mills, and prove by direct comparison to a perturbative SO(6) calculations that our generalization is valid.

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arXiv2012

Holographic 3-point function at one loop

We explore the recent weak/strong coupling match of three-point functions in the AdS/CFT correspondence for two semi-classical operators and one light chiral primary operator found by Escobedo et al. This match is between the tree-level three-point function with the two semi-classical operators described by coherent states while on the string side the three-point function is found in the Frolov-Tseytlin limit. We compute the one-loop correction to the three-point function on the gauge theory side and compare this to the corresponding correction on the string theory side. We find that the corrections do not match. Finally, we discuss the possibility of further contributions on the gauge theory side that can alter our results.

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