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-Type Anomalies Can Depend on Marginal Couplings

Herzog, Christopher P.; Shamir, Itamar

doi:10.1103/physrevlett.124.011601

Cited by 19 publications

(29 citation statements)

References 46 publications

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“…Taking α = 2 in (4. 68) we see that the condition n > 1 2 α + 1 removes the b0 andb 0 terms from the sum, and we recover the α = 0 OPE, as expected from (4.57). If b0 =b 0 = 0 the spectrum would be continuous at α = 2, and all quantities computed with the α < 2 assumption evaluated at α = 2 would yield the α = 0 result.…”

Section: Jhep06(2020)056supporting

confidence: 81%

“…The b coefficient, associated to a A-type anomaly, is determined by the expectation value of the spherical defect and it was shown to be monotonically decreasing under defect RG flows [67]. This prevents its dependence JHEP06(2020)056 on defect marginal couplings, although it still allows for a non-trivial dependence on the bulk marginal parameters [68,69]. This dependence was shown to be absent in the case of supersymmetric defects preserving at least two supercharges of opposite chirality [69].…”

Section: Weyl Anomaly Coefficientsmentioning

confidence: 99%

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Superconformal surfaces in four dimensions

Bianchi

Lemos

2020

J. High Energ. Phys.

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We study the constraints of superconformal symmetry on codimension two defects in four-dimensional superconformal field theories. We show that the one-point function of the stress tensor and the two-point function of the displacement operator are related, and we discuss the consequences of this relation for the Weyl anomaly coefficients as well as in a few examples, including the supersymmetric Rényi entropy. Imposing consistency with existing results, we propose a general relation that could hold for sufficiently supersymmetric defects of arbitrary dimension and codimension. Turning to N = (2, 2) surface defects in N ≥ 2 superconformal field theories, we study the associated chiral algebra. We work out various properties of the modules introduced by the defect in the original chiral algebra. In particular, we find that the one-point function of the stress tensor controls the dimension of the defect identity in chiral algebra, providing a novel way to compute it, once the defect identity is identified. Studying a few examples, we show explicitly how these properties are realized.

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Section: Jhep06(2020)056supporting

confidence: 81%

Section: Weyl Anomaly Coefficientsmentioning

confidence: 99%

Superconformal surfaces in four dimensions

Bianchi

Lemos

2020

J. High Energ. Phys.

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“…Among other things, the classification means b cannot depend on defect marginal couplings, while d 1 and d 2 can. In general, all three can depend on marginal couplings of the ambient CFT [29,30], unless the defect preserves 2d N = (2, 0) SUSY, in which case b cannot depend on ambient marginal couplings either [31]. The central charge b obeys a c-theorem for defect RG flows [19,20], sometimes called the "b-theorem."…”

Section: Jhep05(2020)095mentioning

confidence: 99%

Central charges of 2d superconformal defects

Chalabi

O’Bannon

Robinson

et al. 2020

J. High Energ. Phys.

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In conformal field theories (CFTs) of dimension d > 3, two-dimensional (2d) conformal defects are characterised in part by central charges defined via the defect's contribution to the trace anomaly. However, in general for interacting CFTs these central charges are difficult to calculate. For superconformal 2d defects in supersymmetric (SUSY) CFTs (SCFTs), we show how to compute these defect central charges from the SUSY partition function either on S d with defect along S 2 , or on S 1 × S d−1 with defect along S 1 × S 1. In the latter case we propose that defect central charges appear in an overall normalisation factor, as part of the SUSY Casimir energy. For 2d half-BPS defects in 4d N = 2 SCFTs and in the 6d N = (2, 0) SCFT we obtain novel, exact results for defect central charges using existing results for partition functions computed using SUSY localisation, SUSY indices, and correspondences to 2d Liouville, Toda, and q-deformed Yang-Mills theories. Some of our results for defect central charges agree with those obtained previously via holography, showing that the latter are not just large-N and/or strongcoupling limits, but are exact. Our methods can be straightforwardly extended to other superconformal defects, of various codimension, as we demonstrate for a 4d defect in the 6d N = (2, 0) SCFT.

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“…However, there is a loophole concerning F ∂ , as one of us showed in refs. [55,56]. While F ∂ is not expected to depend on boundary marginal deformations, it can depend on bulk ones.…”

Section: Discussionmentioning

confidence: 96%

Duality and transport for supersymmetric graphene from the hemisphere partition function

2020

Self Cite

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We use localization to compute the partition function of a four dimensional, supersymmetric, abelian gauge theory on a hemisphere coupled to charged matter on the boundary. Our theory has eight real supercharges in the bulk of which four are broken by the presence of the boundary. The main result is that the partition function is identical to that of N = 2 abelian Chern-Simons theory on a three-sphere coupled to chiral multiplets, but where the quantized Chern-Simons level is replaced by an arbitrary complexified gauge coupling τ. The localization reduces the path integral to a single ordinary integral over a real variable. This integral in turn allows us to calculate the scaling dimensions of certain protected operators and two-point functions of abelian symmetry currents at arbitrary values of τ. Because the underlying theory has conformal symmetry, the current two-point functions tell us the zero temperature conductivity of the Lorentzian versions of these theories at any value of the coupling. We comment on S-dualities which relate different theories of supersymmetric graphene. We identify a couple of self-dual theories for which the complexified conductivity associated to the U(1) gauge symmetry is τ /2.

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How a -Type Anomalies Can Depend on Marginal Couplings

Cited by 19 publications

References 46 publications

Superconformal surfaces in four dimensions

Superconformal surfaces in four dimensions

Central charges of 2d superconformal defects

Duality and transport for supersymmetric graphene from the hemisphere partition function

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