TY - JOUR

T1 - Coupling constant dependence in the thermodynamics of script N = 4 supersymmetric Yang-Mills theory

AU - Gubser, Steven S.

AU - Klebanov, Igor R.

AU - Tseytlin, Arkady A.

N1 - Funding Information: We are grateful to H. Liu, A. Rajaraman and E. Witten for discussions and to Yu.N. Obukhov for his kind help with the GRG computer algebra system \[59\].T he work of I.R.K. and S,S.G. was supported in part by US Department of Energy grant DE-FG02-91ER40671 and by the James S. McDonnell Foundation Grant No. 91-48. S.S.G. also thanks the Hertz Foundation for its support. The work of A.A.T. was supported in part by PPARC, the European Commission TMR programme grant ERBFMRX-CT96-0045 and the INTAS grant No. 96-538.

PY - 1998/11/23

Y1 - 1998/11/23

N2 - The free energy of the maximally supersymmetric SU(N) gauge theory at temperature T is expected to scale, in the large-N limit, as N2T4 times a function of the 't Hooft coupling, f(g2YMN). In the strong coupling limit the free energy has been deduced from the near-extremal 3-brane geometry, and its normalization has turned out to be 3/4 times that found in the weak coupling limit. In this paper we calculate the leading correction to this result in inverse powers of the coupling, which originates from the R4 terms in the tree-level effective action of type IIB string theory. The correction to 3/4 is positive and of order (g2YMN)-3/2. Thus, f(g2YMN) increases as the 't Hooft coupling is decreased, in accordance with the expectation that it should be approaching 1 in the weak coupling limit. We also discuss similar corrections for other conformal theories describing coincident branes. In particular, we suggest that the coupling independence of the near extremal entropy for D1-branes bound to D5-branes is related to the vanishing of the Weyl tensor of AdS3 × S3.

AB - The free energy of the maximally supersymmetric SU(N) gauge theory at temperature T is expected to scale, in the large-N limit, as N2T4 times a function of the 't Hooft coupling, f(g2YMN). In the strong coupling limit the free energy has been deduced from the near-extremal 3-brane geometry, and its normalization has turned out to be 3/4 times that found in the weak coupling limit. In this paper we calculate the leading correction to this result in inverse powers of the coupling, which originates from the R4 terms in the tree-level effective action of type IIB string theory. The correction to 3/4 is positive and of order (g2YMN)-3/2. Thus, f(g2YMN) increases as the 't Hooft coupling is decreased, in accordance with the expectation that it should be approaching 1 in the weak coupling limit. We also discuss similar corrections for other conformal theories describing coincident branes. In particular, we suggest that the coupling independence of the near extremal entropy for D1-branes bound to D5-branes is related to the vanishing of the Weyl tensor of AdS3 × S3.

KW - Anti-de Sitter space

KW - Black holes

KW - Large-N limit

KW - String theory

KW - Supersymmetric Yang-Mills theory

KW - Threebranes

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U2 - https://doi.org/10.1016/S0550-3213(98)00514-8

DO - https://doi.org/10.1016/S0550-3213(98)00514-8

M3 - Article

VL - 534

SP - 202

EP - 222

JO - Nuclear Physics, Section B

JF - Nuclear Physics, Section B

SN - 0550-3213

IS - 1-2

ER -