Scalar Correlators in Bosonic Chern-Simons Vector Models

Yacoby, Ran

doi:10.48550/arxiv.1805.11627

Cited by 8 publications

(17 citation statements)

References 20 publications

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“…In order to evaluate the results, we utilize two interesting techniques. The first technique involves inversion of all the momenta appearing in the integral (See appendix.A.1 and section 5.3.2 of [36] and [37]). Through this method one may compute three dimensional box integrals in momentum space easily and efficiently.…”

Section: Four Point Functionsmentioning

confidence: 99%

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Momentum space spinning correlators and higher spin equations in three dimensions

Jain,

John,

Malvimat

2020

Preprint

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In this article, we explicitly compute three and four point momentum space correlation functions involving scalars and spinning operators in the free bosonic and the free fermionic theory in three dimensions. We also evaluate the five point function of scalars in the free bosonic theory. We discuss techniques which are more efficient than the usual PV reduction to evaluate one loop integrals. Our techniques may be easily generalized to momentum space correlators involving complicated spinning operators and to higher point functions. Three dimensional fermionic theory has an interesting feature that the scalar operator ψψ is odd under parity. To account for this feature, we develop a parity odd basis which is useful to write correlation functions involving spinning operators and an odd number of ψψ operators. We further study higher spin (HS) equations in momentum space which are algebraic in nature and hence simpler than their position space counterparts. We use HS equation to solve for specific three point functions involving spinning operators without invoking conformal invariance. However, at the level of four point functions we could only verify our explicit results. We observe that solving for the four point functions requires additional constraints that come from conformal invariance.

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Section: Four Point Functionsmentioning

confidence: 99%

“…For the box scalar integration (A.4), we have used inversion technique used in [36,37]. This technique involves inverting all the momenta including the integration variable as follows l µ = lµ l2 and p i = Pi P 2 (i = 1, 2, 3).…”

Section: A Compendium Of Integralsmentioning

confidence: 99%

Momentum space spinning correlators and higher spin equations in three dimensions

Jain,

John,

Malvimat

2020

Preprint

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“…n,s . At order 1/N it is not known how to directly compute the four-point function of the CS theories by field theory methods, though it is known in some specific kinematic regimes [7,14,15]. However, one can determine the correlation function almost uniquely just from bootstrap considerations.…”

Section: Introductionmentioning

confidence: 99%

The analytic bootstrap for large N Chern-Simons vector models

Aharony

Alday

Bissi

et al. 2018

J. High Energ. Phys.

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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 doubletrace 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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“…Here we will determine the same for the quasi-bosonic theory. The four point function of the scalar operator has been studied in a specific kinematic and parameter regime in [55,59]. Recently, it was demonstrated that in the large-N limit, this correlation function in position space is determined by the free theory answer upto a conformal partial wave which is given by a certain D function as follows [89]…”

Section: Four Point Functionmentioning

confidence: 99%

Constraining momentum space correlators using slightly broken higher spin symmetry

Jain,

John,

Malvimat

2020

Preprint

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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-bosonic and quasi-fermionic theories. At the level of two point functions we show that in addition to the well known parity even contribution the correlator also contains a conformally invariant parity odd contribution whose coupling constant dependence is universal. We also show that higher spin equations solve for three point correlators and match it with known results in the literature obtained only in specific kinematic regimes by intricate direct Feynman diagram computations. In this process we also show how contact terms are necessary to solve the higher spin equations and how their coefficients are fixed. At the level of four point spinning correlators the direct Feynman diagram approach or solving conformal Ward identities in momentum space are difficult and have not been well explored. We show that one can circumvent these difficulties by using higher spin equations to explicitly compute spinning four-point correlators in the interacting theory.One of the interesting facts about higher spin equations is that one can use them away from the conformal fixed point. We illustrate this by considering mass deformed free bosonic theory and solving for two-point functions of spinning operators using higher spin equations.

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Scalar Correlators in Bosonic Chern-Simons Vector Models

Cited by 8 publications

References 20 publications

Momentum space spinning correlators and higher spin equations in three dimensions

Momentum space spinning correlators and higher spin equations in three dimensions

The analytic bootstrap for large N Chern-Simons vector models

Constraining momentum space correlators using slightly broken higher spin symmetry

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