Surface defect, anomalies and b-extremization

Self Cite

Conformal defects describe the universal behaviors of a conformal field theory (CFT) in the presence of a boundary or more general impurities. The coupled critical system is characterized by new conformal anomalies which are analogous to, and generalize those of standalone CFTs. Here we study the conformal a- and c-anomalies of four dimensional defects in CFTs of general spacetime dimensions greater than four. We prove that under unitary defect renormalization group (RG) flows, the defect a-anomaly must decrease, thus establishing the defect a-theorem. For conformal defects preserving minimal supersymmetry, the full defect symmetry contains a distinguished U(1)R subgroup. We derive the anomaly multiplet relations that express the defect a- and c-anomalies in terms of the defect (mixed) ’t Hooft anomalies for this U(1)R symmetry. Once the U(1)R symmetry is identified using the defect a-maximization principle which we prove, this enables a non-perturbative pathway to the conformal anomalies of strongly coupled defects. We illustrate our methods by discussing a number of examples including boundaries in five dimensions and codimension-two defects in six dimensions. We also comment on chiral algebra sectors of defect operator algebras and potential conformal collider bounds on defect anomalies.

Section: Jhep02(2022)061mentioning

confidence: 99%

Defect a-theorem and a-maximization

Wang

2022

Self Cite

“…This is analogous to the prescription dependence in defining the normalisation of local operators as the number C in O(x)O(y) ∼ C/|x − y| 2∆ . In recent years a lot of progress has been achieved in the exact evaluation of the coefficients entering the anomaly of surface operators of the N = (2, 0) theory [20][21][22][23][24][25], so the time is now ripe to turn to evaluating finite expectation values for "anomaless" surfaces, the cases where the anomaly vanishes.…”

Section: Introduction and Conclusionmentioning

confidence: 99%

M2-doughnuts

Drukker

Trépanier

2022

We present a family of new M2-brane solutions in AdS7× S4 that calculate toroidal BPS surface operators in the $$ \mathcal{N} $$ N = (2, 0) theory. These observables are conformally invariant and not subject to anomalies so we are able to evaluate their finite expectation values at leading order at large N. In the limit of a thin torus we find a cylinder, which is a natural surface generalization of both the circular and parallel lines Wilson loop. We study and comment on this limit in some detail.

“…For example, in refs. [39,114], Wang showed for superconformal defects with p = 2 and p = 4 that a Σ is fixed by certain 't Hooft anomaly coefficients, and obeys a form of c-or a-extremization [4,115,116], respectively. Are other defect/boundary central charges fixed by 't Hooft anomaly coefficients?…”

Section: Discussionmentioning

confidence: 99%

“…In a d = 4 SCFT, a p = 2 defect that preserves at least N = (2, 0) two-dimensional SUSY has d 1 = d 2 , which is conjectured to extend to p = 2 defects in d > 4 SCFTs as well [113]. Furthermore, for such defects in a SCFT with d ≥ 3, a (2d) Σ is fixed by an 't Hooft anomaly [114], hence the IR defect R-symmetry can be identified by extremizing a trial a (2d) Σ , similar to a-maximization [4] or c-extremization [115,116].…”

Section: 24)mentioning

confidence: 96%

Weyl anomalies of four dimensional conformal boundaries and defects

Chalabi

Herzog

O’Bannon

et al. 2022

Motivated by questions about quantum information and classification of quantum field theories, we consider Conformal Field Theories (CFTs) in spacetime dimension d ≥ 5 with a conformally-invariant spatial boundary (BCFTs) or 4-dimensional conformal defect (DCFTs). We determine the boundary or defect contribution to the Weyl anomaly using the standard algorithm, which includes imposing Wess-Zumino consistency and fixing finite counterterms. These boundary/defect contributions are built from the intrinsic and extrinsic curvatures, as well as the pullback of the ambient CFT’s Weyl tensor. For a co-dimension one boundary or defect (i.e. d = 5), we reproduce the 9 parity-even terms found by Astaneh and Solodukhin, and we discover 3 parity-odd terms. For larger co-dimension, we find 23 parity-even terms and 6 parity-odd terms. The coefficient of each term defines a “central charge” that characterizes the BCFT or DCFT. We show how several of the parity-even central charges enter physical observables, namely the displacement operator two-point function, the stress-tensor one-point function, and the universal part of the entanglement entropy. We compute several parity-even central charges in tractable examples: monodromy and conical defects of free, massless scalars and Dirac fermions in d = 6; probe branes in Anti-de Sitter (AdS) space dual to defects in CFTs with d ≥ 6; and Takayanagi’s AdS/BCFT with d = 5. We demonstrate that several of our examples obey the boundary/defect a-theorem, as expected.