The exact superconformal R-symmetry maximizes a

By K. Intriligator, B. Wecht. 2003

727 citations recorded by the source corpus.

Abstract An exact and general solution is presented for a previously open problem. We show that the superconformal R-symmetry of any 4d SCFT is exactly and uniquely determined by a maximization principle: it is the R-symmetry, among all possibilities, which (locally) maximizes the combination of 't Hooft anomalies atrial(R)≡(9TrR3−3TrR)/32. The maximal value of atrial is then, by a result of Anselmi et al. the central charge a of the SCFT. Our atrial maximization principle almost immediately ensures that the central charge a decreases upon any RG flow, since relevant deformations force atrial to be maximized over a subset of the previously possible R-symmetries. Using atrial maximization, we find the exact superconformal R-symmetry (and thus the exact anomalous dimensions of all chiral operators) in a variety of previously mysterious 4d N =1 SCFTs. As a check, we verify that our exact results reproduce the perturbative anomalous dimensions in all perturbatively accessible RG fixed points. Our result implies that N =1 SCFTs are algebraic: the exact scaling dimensions of all chiral primary operators, and the central charges a and c, are always algebraic numbers.

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Citations in the corpus

Two-dimensional SCFTs from wrapped branes and c-extremization (2013, background): “ric statement for the compact seven or eight-dimensional manifolds on which we compactify string or M-theory to AdS 3, similarly to [91,92]. After having established a-maximization in four dimensions [8], F-maximization in three dimensions [9,10] and c-extremization in two dimensions [1], it is natu”
AdS 3 solutions of IIB supergravity from D3-branes (2005, methodology): “In particular, the field theory computation of Weyl anomaly using the a-maximization method [4] is shown to agree with the volume of toric Sasaki-Einstein manifolds through Z-minimization developed in [5].”
Spontaneous Breaking of Conformal Invariance and Trace Anomaly Matching (2010, background): “The massive flows relate by definition conformal theories in the ultraviolet and infrared but the trace anomalies of the two theories are not matched: rather the flow has the property that the a-trace anomaly coefficient decreases along it [2].”
Tilings, Chern-Simons Theories and M2 Branes (2008, result): “In the 3+1 dimensional case, we can explicitly compare the results of a-maximization [37, 38] with the spectrum of dimensions computed from volumes of cycles in H and gain confidence in our identification of the quiver gauge theory as the dual of AdS4×H [39, 40, 41, 42, 43].”
Towards a derivation of holographic entanglement entropy (2011, background): “In particular, as function of possible trial R-charges, (the finite part of) Z is extremized by the exact superconformal R-charge, in analogy to a-maximization in four dimensions [51].”
Toric Geometry, Sasaki–Einstein Manifolds and a New Infinite Class of AdS/CFT Duals (2004, methodology): “Recall that, as proposed in [9], the R-symmetry mixes with the abelian flavour symmetries maximising, among all such admissible R-symmetries, a certain combination of ‘t Hooft anomalies.”
The large N limit of quiver matrix models and Sasaki-Einstein manifolds (2011, background): “For the latter theories, the exact NSVZ beta functions and a-maximization [12] provide stringent constraints on the R-symmetry of superconformal theories, and indeed allow one to unambiguosly determine R-charges and related trace anomaly coefficients in most cases.”
Supersymmetry on curved spaces and holography (2012, background): “This solved a longstanding problem in conformal field theory, as it had been predicted from gravity [16] that, at least for SCFTs with a gravity dual, some analogue principle to the a-maximisation in 4d [17] should exist also in 3d.”
Supersymmetric AdS5 solutions of type IIB supergravity (2005, background): “Furthermore, if the local solutions were to somehow make physical sense, some restrictions on p would have to be imposed to ensure an algebraic central charge as implied by the general results on a-maximization [47].”
The holographic dual of AdS3 × S3 × S3 × S1 (2014, methodology): “This can be repackaged as a statement of c-extremisation [21, 22], in analogy to the story of a-maximisation in four dimensions [23] How to apply the discussion above to our N = (0, 4) theory? Now the R-symmetries are no longer Abelian.”
M5-branes from gauge theories on the 5-sphere (2012, result): “It is interesting to compare this with the a and c central charges of the SCFT, given by [56–58]”
Emergent spacetime and holographic CFTs (2011, background): “In supersymmetric theories this result has even been partially demonstrated [114] using the fact that these coefficients are related via anomaly computations to the R-symmetry charges.”
Holography, Entanglement Entropy, and Conformal Field Theories with Boundaries or Defects (2013, unknown): “Thanks to N = 1 superconformal symmetry, this result for a is independent of λ [78, 79], and indeed this result for a agrees with the free field result (N2 − 1)/(64π2) in the large-N limit.”
Obstructions to the Existence of Sasaki–Einstein Metrics (2006, methodology): “Indeed, the R–charges of fields may be computed using a–maximisation [14], and agree with the naive geometric computations, assuming that the Sasaki–Einstein metrics on L2p exist.”