Improved Wald formalism and First Law of Dyonic Black Strings with Mixed Chern-Simons Terms

Abstract

We study the first law of thermodynamics of dyonic black strings carrying a linear momentum in type IIA string theory compactified on K3 with leading order ${\alpha }^{\prime }$ corrections. The low energy effective action contains mixed Chern-Simons terms of the form $-2B_{(2)}\wedge \mathrm{tr}(R({\Gamma }_{\pm })\wedge R({\Gamma }_{\pm }))$ which is equivalent to $2H_{(3)}\wedge {\mathrm{CS}}_{(3)}({\Gamma }_{\pm })$ up to a total derivative. We find that the naive application of Wald entropy formula leads to two different answers associated with the two formulations of the mixed Chern-Simons terms. Surprisingly, neither of them satisfies the first law of thermodynamics for other conserved charges computed unambiguously using the standard methods. We resolve this problem by carefully evaluating the full infinitesimal Hamiltonian at both infinity and horizon, including contributions from terms proportional to the Killing vector which turn out to be nonvanishing on the horizon and indispensable to establish the first law. We find that the infinitesimal Hamiltionian associated with $-2B_{(2)}\wedge \mathrm{tr}(R({\Gamma }_{\pm })\wedge R({\Gamma }_{\pm }))$ requires an improvement via adding a closed but non-exact term, which vanishes when the string does not carry either the magnetic charge or linear momentum. Consequently, both formulations of the mixed Chern-Simons terms yield the same result of the entropy that however does not agree with the Wald entropy formula. In the case of extremal black strings, we also contrast our result with the one obtained from Sen's approach.

arXiv commentLatex, 27 pages, adding discussions on attractor mechanism, to appear in JHEP

References in corpus (31)

• Black Hole Entropy is Noether Charge
• The Dynamics of General Relativity
• Some Properties of Noether Charge and a Proposal for Dynamical Black Hole Entropy
• Quasilocal Energy and Conserved Charges Derived from the Gravitational Action
• Unity of Superstring Dualities
• A General Definition of "Conserved Quantities" in General Relativity and Other Theories of Gravity
• Covariant theory of asymptotic symmetries, conservation laws and central charges
• Energy in Generic Higher Curvature Gravity Theories
• Black Hole Entropy in the presence of Chern-Simons Terms
• Quasilocal mass in general relativity
• AdS Dyonic Black Hole and its Thermodynamics
• Higher-derivative couplings in string theory: dualities and the B-field
• Quasi-Local Conserved Charges in Covariant Theory of Gravity
• String Theory in Magnetic Monopole Backgrounds
• The Role of Dipole Charges in Black Hole Thermodynamics
• Higher derivative corrections to Kerr black hole thermodynamics
• Black holes in five-dimensional gauged supergravity with higher derivatives
• All Off-Shell R^2 Invariants in Five Dimensional N=2 Supergravity
• Precision Entropy of Spinning Black Holes
• Thermodynamics of Magnetised Kerr-Newman Black Holes
• Note on the First Law with p-form potentials
• AdS${}_5$ Holography and Higher-Derivative Supergravity
• The first law and Wald entropy formula of heterotic stringy black holes at first order in alpha prime
• Gauss-Bonnet supergravity in six dimensions
• Gravitational Chern-Simons Lagrangians and black hole entropy
• Curvature squared invariants in six-dimensional $\mathcal{N}=(1,0)$ supergravity
• First Law of Black Rings Thermodynamics in Higher Dimensional Chern-Simons Gravity
• Covariant Noether Charge for Higher Dimensional Chern-Simons Terms
• Attractor Mechanism and Non-Renormalization Theorem in 6D (1,0) Supergravity
• Rotating Strings in Six-Dimensional Higher-Derivative Supergravity
• First Law of Black Hole in the Gravitational Electromagnetic System

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• Negative Corrections to Black Hole Entropy from String Theory
• Dyonic Black Strings and the Charge Lattice in Salam-Sezgin model