Equivalence of a-maximization and volume minimization

Eager, Richard

doi:10.1007/jhep01(2014)089

Cited by 24 publications

(34 citation statements)

References 68 publications

(117 reference statements)

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“…In the field theory they appear in the behavior of the Hilbert series for mesonic operators in the CFT [37]. Therefore, the leading order central charges are encoded in the spectrum as well; our results suggest that they are not, however, encoded in the large-N superconformal index.…”

Section: Moving Away From Large-nmentioning

confidence: 59%

Central Charges from theN=1Superconformal Index

2015

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We present prescriptions for obtaining the central charges, a and c, of a four dimensional superconformal quantum field theory from the superconformal index. At infinite N , for holographic theories dual to Sasaki-Einstein 5-manifolds the prescriptions give the O(1) parts of the central charges. This allows us, among other things, to show the exact AdS/CFT matching of a and c for arbitrary toric quiver CFTs without adjoint matter that are dual to smooth Sasaki-Einstein 5-manifolds. In addition, we include evidence from non-holographic theories for the applicability of these results outside of a holographic setting and away from the large-N limit.

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Section: Moving Away From Large-nmentioning

confidence: 59%

Central Charges from theN=1Superconformal Index

2015

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“…for a suitable choice of the vertex i [31,23,32]. Here C(x) is the cofactor matrix of χ(x), and is polynomial in bx.…”

Section: Factorization For Toric Calabi-yausmentioning

confidence: 99%

Superconformal indices, Sasaki-Einstein manifolds, and cyclic homologies

Eager

Schmude

Tachikawa

2014

Advances in Theoretical and Mathematical Physics

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The superconformal index of the quiver gauge theory dual to type IIB string theory on the product of an arbitrary smooth Sasaki-Einstein manifold with five-dimensional AdS space is calculated both from the gauge theory and gravity viewpoints. We find complete agreement. Along the way, we find that the index on the gravity side can be expressed in terms of the Kohn-Rossi cohomology of the Sasaki-Einstein manifold and that the index of a quiver gauge theory equals the Euler characteristic of the cyclic homology of the Ginzburg dg algebra associated to the quiver.

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“…The superconformal index and the central charge a of four-dimensional superconformal field theories are invariants of their associated Calabi-Yau 3-algebra [13,38]. It would be very interesting to find a similar mathematical structure governing three-dimensional quiver Chern-Simons theories.…”

Section: Jhep12(2015)062mentioning

confidence: 99%

Superconformal indices and M2-branes

Eager

Schmude

2015

J. High Energ. Phys.

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Abstract:We derive the superconformal index of the world-volume theory on M2-branes probing the cone over an arbitrary Sasaki-Einstein seven-manifold. The index is expressed in terms of the cohomology groups of the cone. We match our supergravity results with known results from gauge theory. Along the way we derive the spectrum of short KaluzaKlein multiplets on generic Sasaki-Einstein seven-manifolds.

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Equivalence of a-maximization and volume minimization

Cited by 24 publications

References 68 publications

Central Charges from theN=1Superconformal Index

Central Charges from theN=1Superconformal Index

Superconformal indices, Sasaki-Einstein manifolds, and cyclic homologies

Superconformal indices and M2-branes

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