Correlation functions of Coulomb branch operators

Gerchkovitz, Efrat; Gomis, Joaquim; Ishtiaque, Nafiz; Karasik, Avner; Komargodski, Zohar; Pufu, Silviu S.

doi:10.1007/jhep01(2017)103

Cited by 151 publications

(392 citation statements)

References 67 publications

(178 reference statements)

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“…The latter is in turn completely determined by the two-and three-point functions of chiral primary operators [8]. Thanks to recent developments, these correlation functions are now computable in several 4d N = 2 SCFTs [9,10,[24][25][26][27][28][29]. Therefore, these results can now be interpreted as an exact determination of the Berry curvature for the chiral primary states of these theories.…”

Section: Berry Phase In 4d N = 2 Scftsmentioning

confidence: 97%

Aspects of Berry phase in QFT

Baggio

Niarchos

Papadodimas

2017

J. High Energ. Phys.

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When continuous parameters in a QFT are varied adiabatically, quantum states typically undergo mixing -a phenomenon characterized by the Berry phase. We initiate a systematic analysis of the Berry phase in QFT using standard quantum mechanics methods. We show that a non-trivial Berry phase appears in many familiar QFTs. We study a variety of examples including free electromagnetism with a theta angle, and certain supersymmetric QFTs in two and four spacetime dimensions. We also argue that a large class of QFTs with rich Berry properties is provided by CFTs with non-trivial conformal manifolds. Using the operator-state correspondence we demonstrate in this case that the Berry connection is equivalent to the connection on the conformal manifold derived previously in conformal perturbation theory. In the special case of chiral primary states in 2d N = (2, 2) and 4d N = 2 SCFTs the Berry phase is governed by the tt * equations. We present a technically useful rederivation of these equations using quantum mechanics methods.

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Section: Berry Phase In 4d N = 2 Scftsmentioning

confidence: 97%

Aspects of Berry phase in QFT

Baggio

Niarchos

Papadodimas

2017

J. High Energ. Phys.

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“…The reason is that on S 2 , compared to 2 , we have operators mixing with lower dimensional ones, 5 see [53], in particular Σ andΣ mix with the identity. The determinant of the matrix g removes this mixing and produces the only relevant correlator for 1 given by the connected correlator…”

Section: Chiral Ring Formentioning

confidence: 99%

“…If we consider the difference between the perturbative coefficients in the k = 1 non-perturbative sector, easily obtained from (51)(52)(53)(54)(55), and the asymptotic approximation just defined we have…”

Section: Large Orders Relationsmentioning

confidence: 99%

The grin of Cheshire cat resurgence from supersymmetric localization

Dorigoni

Glass

2018

SciPost Phys.

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First we compute the S 2 partition function of the supersymmetric N −1 model via localization and as a check we show that the chiral ring structure can be correctly reproduced. For the 1 case we provide a concrete realisation of this ring in terms of Bessel functions. We consider a weak coupling expansion in each topological sector and write it as a finite number of perturbative corrections plus an infinite series of instantonanti-instanton contributions. To be able to apply resurgent analysis we then consider a non-supersymmetric deformation of the localized model by introducing a small unbalance between the number of bosons and fermions. The perturbative expansion of the deformed model becomes asymptotic and we analyse it within the framework of resurgence theory. Although the perturbative series truncates when we send the deformation parameter to zero we can still reconstruct non-perturbative physics out of the perturbative data in a nice example of Cheshire cat resurgence in quantum field theory. We also show that the same type of resurgence takes place when we consider an analytic continuation in the number of chiral fields from N to r ∈ . Although for generic real r supersymmetry is still formally preserved, we find that the perturbative expansion of the supersymmetric partition function becomes asymptotic so that we can use resurgent analysis and only at the end take the limit of integer r to recover the undeformed model.

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“…chiral correlators [29][30][31][32][33][34], Wilson loop expectation values [4,35,36], the radiation emitted by a heavy quark [37,38], or other protected subsectors of operators [39]. It would be very interesting to import these results to 6D, and compare where possible with other approaches to the (2,0) theory.…”

Section: Jhep06(2017)072mentioning

confidence: 99%

Exact deconstruction of the 6D (2,0) theory

Hayling

Papageorgakis

Pomoni³

et al. 2017

J. High Energ. Phys.

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Abstract:The dimensional-deconstruction prescription of Arkani-Hamed, Cohen, Kaplan, Karch and Motl provides a mechanism for recovering the A-type (2,0) theories on T 2 , starting from a four-dimensional N = 2 circular-quiver theory. We put this conjecture to the test using two exact-counting arguments: in the decompactification limit, we compare the Higgs-branch Hilbert series of the 4D N = 2 quiver to the "half-BPS" limit of the (2,0) superconformal index. We also compare the full partition function for the 4D quiver on S 4 to the (2,0) partition function on S 4 × T 2 . In both cases we find exact agreement. The partition function calculation sets up a dictionary between exact results in 4D and 6D.

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Correlation functions of Coulomb branch operators

Cited by 151 publications

References 67 publications

Aspects of Berry phase in QFT

Aspects of Berry phase in QFT

The grin of Cheshire cat resurgence from supersymmetric localization

Exact deconstruction of the 6D (2,0) theory

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