TY - JOUR
T1 - Toric geometry and the dual of c-extremization
AU - Gauntlett, Jerome P.
AU - Martelli, Dario
AU - Sparks, James
PY - 2019/1/28
Y1 - 2019/1/28
N2 - We consider D3-brane gauge theories at an arbitrary toric Calabi-Yau 3-fold cone singularity that are then further compactified on a Riemann surface Σg, with an arbitrary partial topological twist for the global U(1) symmetries. This constitutes a rich, infinite class of two-dimensional (0, 2) theories. Under the assumption that such a theory flows to a SCFT, we show that the supergravity formulas for the central charge and R-charges of BPS baryonic operators of the dual AdS3 solution may be computed using only the toric data of the Calabi-Yau 3-fold and the topological twist parameters. We exemplify the procedure for both the Yp,q and Xp,q 3-fold singularities, along with their associated dual quiver gauge theories, showing that the new supergravity results perfectly match the field theory results obtained using c-extremization, for arbitrary twist over Σg. We furthermore conjecture that the trial central charge [InlineMediaObject not available: see fulltext.], which we define in gravity, matches the field theory trial c-function off-shell, and show this holds in non-trivial examples. Finally, we check our general geometric formulae against a number of explicitly known supergravity solutions.
AB - We consider D3-brane gauge theories at an arbitrary toric Calabi-Yau 3-fold cone singularity that are then further compactified on a Riemann surface Σg, with an arbitrary partial topological twist for the global U(1) symmetries. This constitutes a rich, infinite class of two-dimensional (0, 2) theories. Under the assumption that such a theory flows to a SCFT, we show that the supergravity formulas for the central charge and R-charges of BPS baryonic operators of the dual AdS3 solution may be computed using only the toric data of the Calabi-Yau 3-fold and the topological twist parameters. We exemplify the procedure for both the Yp,q and Xp,q 3-fold singularities, along with their associated dual quiver gauge theories, showing that the new supergravity results perfectly match the field theory results obtained using c-extremization, for arbitrary twist over Σg. We furthermore conjecture that the trial central charge [InlineMediaObject not available: see fulltext.], which we define in gravity, matches the field theory trial c-function off-shell, and show this holds in non-trivial examples. Finally, we check our general geometric formulae against a number of explicitly known supergravity solutions.
KW - AdS-CFT Correspondence
KW - Supersymmetric Gauge Theory
UR - http://www.scopus.com/inward/record.url?scp=85060924314&partnerID=8YFLogxK
U2 - 10.1007/JHEP01(2019)204
DO - 10.1007/JHEP01(2019)204
M3 - Article
AN - SCOPUS:85060924314
SN - 1126-6708
VL - 2019
JO - Journal of High Energy Physics
JF - Journal of High Energy Physics
IS - 1
M1 - 204
ER -