TY - JOUR

T1 - Thermodynamics of noncritical M-theory and the topological A-model

AU - Hořava, Petr

AU - Keeler, Cynthia A.

N1 - Funding Information:
We wish to thank Mina Aganagic, Ofer Aharony, Sumit Das, Eric Gimon and Aleksey Mints for useful discussions. This material is based upon work supported by NSF grant PHY-0244900, DOE grant DE-AC02-05CH11231, an NSF Graduate Research Fellowship, and the Berkeley Center for Theoretical Physics.

PY - 2006/6/19

Y1 - 2006/6/19

N2 - In [P. Hořava, C.A. Keeler, Noncritical M-theory in 2 + 1 dimensions as a nonrelativistic Fermi liquid, hep-th/0508024], noncritical M-theory for two-dimensional type 0A and 0B strings was defined in terms of a double-scaled theory of nonrelativistic fermions in 2 + 1 dimensions. Here we study this noncritical M-theory at finite temperature. We derive the exact expression for the free energy of its vacuum solution, as a function of a coupling constant gM and the radius R of the thermal circle. We show that at high temperature, the theory is effectively described by another M-theory solution, whose effective loop-counting coupling scales in a novel way characteristic of M-theory, as T3. Our calculations further suggest that noncritical M-theory is dual to the closed string theory of the topological A-model on a Calabi-Yau, with the radius R of the Euclidean time circle in M-theory playing the role of the string coupling constant of the A-model. In this correspondence, T-duality on the Euclidean time circle of noncritical M-theory implies an S-duality for the topological A-model.

AB - In [P. Hořava, C.A. Keeler, Noncritical M-theory in 2 + 1 dimensions as a nonrelativistic Fermi liquid, hep-th/0508024], noncritical M-theory for two-dimensional type 0A and 0B strings was defined in terms of a double-scaled theory of nonrelativistic fermions in 2 + 1 dimensions. Here we study this noncritical M-theory at finite temperature. We derive the exact expression for the free energy of its vacuum solution, as a function of a coupling constant gM and the radius R of the thermal circle. We show that at high temperature, the theory is effectively described by another M-theory solution, whose effective loop-counting coupling scales in a novel way characteristic of M-theory, as T3. Our calculations further suggest that noncritical M-theory is dual to the closed string theory of the topological A-model on a Calabi-Yau, with the radius R of the Euclidean time circle in M-theory playing the role of the string coupling constant of the A-model. In this correspondence, T-duality on the Euclidean time circle of noncritical M-theory implies an S-duality for the topological A-model.

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U2 - 10.1016/j.nuclphysb.2006.02.039

DO - 10.1016/j.nuclphysb.2006.02.039

M3 - Article

AN - SCOPUS:33646534861

VL - 745

SP - 1

EP - 28

JO - Nuclear Physics B

JF - Nuclear Physics B

SN - 0550-3213

IS - 1-2

ER -