Abstract
We study RG flows between superconformal field theories living in different spacetime dimensions which exhibit universal properties, independent of the details of the UV and IR theories. In particular, when the UV and IR theories are both even-dimensional we establish exact universal relations between their conformal anomaly coefficients. We also provide strong evidence for similar relations between appropriately defined free energies for RG flows between odd-dimensional theories in the large N limit. Holographically, these RG flows across dimensions are described by asymptotically AdS black branes in a gauged supergravity theory, which we exhibit explicitly. We also discuss the uplift of these solutions to string and M-theory and comment on how the entropy of such black branes is captured by the dual field theory.
Highlights
Introduction and summarySupersymmetric quantum field theories (QFTs) placed in background fields provide a rich laboratory for testing our understanding of quantum theories
superconformal field theories (SCFTs) discussed, for example, around table 1 of [61]. These SCFTs are distinguished by having a one-dimensional Coulomb branch of vacua and we summarize the results for the two-dimensional central charges for the three universal twists we have studied so far, namely the α- and β-twists discussed above as well as the universal (0, 2) twist discussed in section 3.2.1, in table 1
As we have argued on general grounds, this four-dimensional black hole can be uplifted to ten- or eleven-dimensional supergravity in infinitely many ways, depending on the choice of internal six- or seven-manifold; each uplift describes the twisted compactification of a different 3d N = 2 SCFT
Summary
Supersymmetric quantum field theories (QFTs) placed in background fields provide a rich laboratory for testing our understanding of quantum theories. The basic observation is that for supersymmetric QFTs with a continuous global R-symmetry one can turn on a background gauge field for this symmetry, and tune its magnitude so as to cancel (part) of the curvature of the manifold This procedure, dubbed a topological twist, ensures that there is a particular covariantly constant spinor defined on the curved background, which can be used as a supersymmetry generator.. This procedure can be interpreted as an RG flow across dimensions, triggered by the local operators in the d-dimensional UV SCFT which are turned on by the background fields implementing the twist This procedure is often applied in the literature to study specific QFTs, and has led to many new insights into the physics of the resulting low energy p-dimensional theory, as well as to unexpected dualities between this theory and a topological theory on Md−p; see [3] for a recent review and further references. We proceed to present a short summary of the main results of our work
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