Gravitational Chern-Simons Term Research Articles

Note on Chern-Simons term correction to holographic entanglement entropy

From the perspective of AdS/CFT correspondence, we study the gravitational Chern-Simons term correction to the holographic entanglement entropy of CFT on the conformal boundary of asymptotically AdS$_3$ spacetime using the off-shell Euclidean path integral method. We show that, like the BTZ black hole entropy, the holographic entanglement entropy is indeed modified due to the gravitational Chern-Simons term although the bulk geometry does not change.

Massive gravity with mass term in three dimensions

We analyze the effect of the Pauli-Fierz mass term on a recently established, new massive gravity theory in three space-time dimensions. We show that the Pauli-Fierz mass term makes the new massive gravity theory nonunitary. Moreover, although we add the gravitational Chern-Simons term to this model, the situation remains unchanged and the theory stays nonunitary despite that the structure of the graviton propagator is greatly changed. Thus, the Pauli-Fierz mass term is not allowed to coexist with mass-generating higher-derivative terms in the new massive gravity.

Note on cosmology of the dimensionally reduced gravitational Chern-Simons term

We present cosmological solutions from the dimensionally reduced Chern-Simons term and obtain the smooth transition solution from the decelerated phase (AdS) to the accelerated phase (dS)

Absorption cross section in warped AdS3black hole

The absorption cross section is studied in the low-frequency region for a propagating scalar field under the warped AdS3 black hole background in the { cosmological} topologically massive gravity. It can be shown that the absorption cross section is { unexpectedly} deformed by the gravitational Chern-Simons term, which is proportional to the scattering area of black hole with an additional contribution depending on the combinations of left-moving and right-moving temperatures. It means that the cross section is larger than the area in spite of the s-wave limit. Finally, we discuss the left-right quasinormal modes for the scalar perturbation in this black hole.

α′-exact entropies for BPS and non-BPS extremal dyonic black holes in heterotic string theory from ten-dimensional supersymmetry

We calculate near-horizon solutions for four-dimensional 4-charge and five-dimensional 3-charge black holes in heterotic string theory from the part of the ten-dimensional tree-level effective action which is connected to gravitational Chern-Simons term by supersymmetry. We obtain that the entropies of large black holes exactly match the α'-exact statistical entropies obtained from microstate counting (D = 4) and AdS/CFT correspondence (D = 5). Especially interesting is that we obtain agreement for both BPS and non-BPS black holes, contrary to the case of R2-truncated (four-derivative) actions (D-dimensional = 2 off-shell supersymmetric or Gauss-Bonnet) were used, which give the entropies agreeing (at best) just for BPS black holes. The key property of the solutions, which enabled us to tackle the action containing infinite number of terms, is vanishing of the Riemann tensor MNPQ obtained from torsional connection defined with = Γ−½H. Moreover, if every monomial of the remaining part of the effective action would contain at least two Riemanns MNPQ, it would trivially follow that our solutions are exact solutions of the full heterotic effective action in D = 10. The above conjecture, which appeared (in this or stronger form) from time to time in the literature, has controversial status, but is supported by the most recent calculations of Richards (arXiv:0807.3453 [hep-th]). Agreement of our results for the entropies with the microscopic ones supports the conjecture. As for small black holes, our solutions in D = 5 still have singular horizons.

Boundary S-matrix in a (2, 0) theory ofAdS3supergravity

We will discuss two inequivalent generalizations of the standard (2, 0) supergravity action [1] to include gravitational Chern-Simons term. One is in the first order formalism where we treat ωMab as independent and the other is in the second order formalism where ωMab is determined in terms of other fields via a standard constraint equation. The two theories have different equations of motion and the solutions to the equations of motion of the first order theory spans only a subset of those of the second order theory. We will be interested in computing the boundary S-matrix, describing correlation functions in a dual conformal field theory, in this sector and hence we use the equations of motion coming out of the first order theory. We restrict ourselves to the gauge+fermionic sector of the theory to compute the boundary S-matrix. We will also look at the effect of higher derivative terms on the boundary S-matrix obtained using the standard supergravity action.

Three-dimensional Chern-Simons black holes

We construct black hole solutions to three-dimensional Einstein-Maxwell theory with both gravitational and electromagnetic Chern-Simons terms. These intrinsically rotating solutions are geodesically complete, and causally regular within a certain parameter range. Their mass, angular momentum and entropy are found to satisfy the first law of black hole thermodynamics. These Chern-Simons black holes admit a four-parameter local isometry algebra, which generically is $sl(2,R)\ifmmode\times\else\texttimes\fi{}R$, and may be generated from the corresponding vacua by local coordinate transformations.

Constraint dynamics and gravitons in three dimensions

The complete non-linear three-dimensional Einstein gravity with gravitational Chern-Simons term and cosmological constant are studied in dreibein formulation. The constraints and their algebras are computed in an explicit form. From counting the number of first and second class constraints, the number of dynamical degrees of freedom, which equals to the number of propagating graviton modes, is found to be 1, "regardless of" the value of cosmological constant. I note also that the usual equivalence with Chern-Simons gauge theory does "not" work for general circumstances.

Ambiguities in the effective action in Lorentz-violating gravity

We investigate the occurrence of ambiguities for the Lorentz-violating gravitational Chern-Simons term. It turns out that this term is accompanied by a coefficient depending on an undetermined parameter, due to an arbitrariness in the choice of the conserved current.

Brown-Henneaux's canonical approach to topologically massive gravity

We analyze the symmetry realized asymptotically on the two dimensional boundary of AdS_3 geometry in topologically massive gravity, which consists of the gravitational Chern-Simons term as well as the usual Einstein-Hilbert and negative cosmological constant terms. Our analysis is based on the conventional canonical method and proceeds along the line completely parallel to the original Brown and Henneaux's. In spite of the presence of the gravitational Chern-Simons term, it is confirmed by the canonical method that the boundary theory actually has the conformal symmetry satisfying the left and right moving Virasoro algebras. The central charges of the Virasoro algebras are computed explicitly and are shown to be left-right asymmetric due to the gravitational Chern-Simons term. It is also argued that the Cardy's formula for the BTZ black hole entropy capturing all higher derivative corrections agrees with the extended version of the Wald's entropy formula. The M5-brane system is illustrated as an application of the present calculation.

BTZ black hole with higher derivatives, the second law of thermodynamics, and statistical entropy: A new proposal

I consider the thermodynamics of the BTZ black hole in the presence of the higher curvature and gravitational Chern-Simons terms, and its statistical entropy. I propose a new thermodynamical entropy, which is manifestly non-negative, such that the second law of thermodynamics is satisfied. I show that the new thermodynamical entropy agrees perfectly with the statistical entropy for all the values of the conformal factor of the higher curvature terms and the coupling constant of the gravitational Chern-Simons term, in contrast to some disagreements in the literature. The agreement with both the higher curvature and gravitational Chern-Simons terms is possible because of an appropriate balancing of them, though it is not a trivial matter because of a conflict in the appropriate Hilbert space for a well-defined conformal field theory for each term.

Holography in three-dimensional Kerr–de Sitter space with a gravitational Chern–Simons term

The holographic description of the three-dimensional Kerr–de Sitter space with a gravitational Chern–Simons term is studied, in the context of dS/CFT correspondence. The space has only one (cosmological) event horizon and its mass and angular momentum are identified from the holographic energy–momentum tensor at the asymptotic infinity. The thermodynamic entropy of the cosmological horizon is computed directly from the first law of thermodynamics, with the conventional Hawking temperature, and it is found that the usual Gibbons–Hawking entropy is modified. It is remarked that, due to the gravitational Chern–Simons term, (a) the results go beyond the analytic continuation from AdS, (b) the maximum-mass/N-bound conjecture may be violated and (c) the three-dimensional cosmology is chiral. A statistical mechanical computation of the entropy, from a Cardy-like formula for a dual CFT at the asymptotic boundary, is discussed. Some remarks on the technical differences in the Chern–Simons energy–momentum tensor, from the literature, are also made.

α′2-corrections to extremal dyonic black holes in heterotic string theory

We calculate α'2-corrections to the entropy of the 5-dimensional 3-charge and the 4-dimensional 4-charge large extremal black holes using the low energy effective action of the heterotic string theory. In the 4-dimensional case, our results are in agreement with the microscopic statistical entropy both for the BPS and the non-BPS black holes. In the more interesting 5-dimensional case, where the direct microscopic stringy description is still unknown, our results for the BPS black holes are in agreement with the results obtained from the action supplemented with R2-correction obtained by supersymmetric completion of the gravitational Chern-Simons term. This agreement does not extend to the non-BPS black holes, for which we propose a different expression for the entropy. We show that the new expression is supported by certain α'3-order calculations, and by the arguments based on the AdS/CFT correspondence.

Banados-Teitelboim-Zanelli black hole with gravitational Chern-Simons term: Thermodynamics and statistical entropy

Recently, the Banados-Teitelboim-Zanelli (BTZ) black hole in the presence of the gravitational Chern-Simons term has been studied, and it is found that the usual thermodynamic quantities, like the black hole mass, angular momentum, and entropy, are modified. But, for large values of the gravitational Chern-Simons coupling where the modification terms dominate the original terms some exotic behaviors occur, like the roles of the mass and angular momentum are interchanged and the entropy depends more on the inner horizon area than the outer one. A basic physical problem of this system is that the form of entropy does not guarantee the second law of thermodynamics, in contrast to the Bekenstein-Hawking entropy. Moreover, this entropy does not agree with the statistical entropy, in contrast to a good agreement for small values of the gravitational Chern-Simons coupling. Here I find that there is another entropy formula where the usual Bekenstein-Hawking form dominates the inner-horizon term again, as in the small gravitational Chern-Simons coupling case, such that the second law of thermodynamics can be guaranteed. I also find that the new entropy formula agrees with the statistical entropy based on the holographic anomalies for the whole range of the gravitational Chern-Simons coupling. This reproduces, in the limit of a vanishing Einstein-Hilbert term, the recent result about the exotic BTZ black holes, where their masses and angular momenta are completely interchanged and the entropies depend only on the area of the inner horizon. I compare the result of the holographic approach with the classical-symmetry-algebra-based approach, and I find exact agreements even with the higher-derivative corrections of the gravitational Chern-Simons term. This provides a nontrivial check of the AdS/CFT correspondence, in the presence of higher-derivative terms in the gravity action.

Circular polarization of primordial gravitational waves in string-inspired inflationary cosmology

We study a mechanism to produce the circular polarization of primordial gravitational waves. The circular polarization is generated during the superinflation driven by the Gauss-Bonnet term in the string-inspired cosmology. The instability in the tensor mode caused by the Gauss-Bonnet term and the parity violation due to the gravitational Chern-Simons term are the essential ingredients of the mechanism. We also discuss detectability of the produced circular polarization of gravitational waves. It turns out that the simple model of single-field inflation contradicts cosmic microwave background (CMB) observations. To circumvent this difficulty, we propose a two-field inflation model. In this two-field model, the circular polarization of gravitational waves is created in the frequency range designed by the big-bang observer (BBO) or the deci-hertz gravitational-wave observatory (DECIGO)

Extremal black holes inD= 5: SUSY vs. Gauss-Bonnet corrections

We analyse near-horizon solutions and compare the results for the black hole entropy of five-dimensional spherically symmetric extremal black holes when the N=2 SUGRA actions are supplied with two different types of higher-order corrections: (1) supersymmetric completion of gravitational Chern-Simons term, and (2) Gauss-Bonnet term. We show that for large BPS black holes lowest order \alpha' corrections to the entropy are the same, but for non-BPS are generally different. We pay special attention to the class of prepotentials connected with K3\times T^2 and T^6 compactifications. For supersymmetric correction we find beside BPS also a set of non-BPS solutions. In the particular case of T^6 compactification (equivalent to the heterotic string on $T^4\times S^1$) we find the (almost) complete set of solutions (with exception of some non-BPS small black holes), and show that entropy of small black holes is different from statistical entropy obtained by counting of microstates of heterotic string theory. We also find complete set of solutions for K3\times T^2 and T^6 case when correction is given by Gauss-Bonnet term. Contrary to four-dimensional case, obtained entropy is different from the one with supersymmetric correction. We show that in Gauss-Bonnet case entropy of small ``BPS'' black holes agrees with microscopic entropy in the known cases.

Black hole entropy in the presence of Chern–Simons terms

We derive a formula for the black hole entropy in theories with gravitational Chern–Simons terms, by generalizing Wald's argument which uses the Noether charge. It correctly reproduces the entropy of three-dimensional black holes in the presence of the Chern–Simons term, which was previously obtained via indirect methods.

4-Dimensional Einstein Gravity Extended by a 3-Dimensional Gravitational Chern-Simons Term

When 4-dimensional general relativity is extended by a 3-dimensional gravitational Chern–Simons term an apparent violation of diffeormorphism invariance is extinguished by the dynamical equations of motion for the modified theory. The physical predictions of this recently proposed model show little evidence of symmetry breaking, but require the vanishing of the Pontryagin density.

Holography with a gravitational Chern-Simons term

The holographic description in the presence of the gravitational Chern-Simons term is studied. The modified gravitational equations are integrated by using the Fefferman-Graham expansion, and the holographic stress-energy tensor is identified. The stress-energy tensor has both conformal anomaly and gravitational or, if reformulated in terms of the zweibein, Lorentz anomaly. We comment on the structure of anomalies in two dimensions and show that the two-dimensional stress-energy tensor can be reproduced by integrating the conformal and gravitational anomalies. We study the black hole entropy in theories with a gravitational Chern-Simons term and find that the usual Bekenstein-Hawking entropy is modified. For the Banados-Teitelboim-Zanelli (BTZ) black hole, the modification is determined by the area of the inner horizon. We show that the total entropy of the BTZ black hole is precisely reproduced in a boundary conformal field theory calculation using the Cardy formula.

BTZ black hole with Chern-Simons and higher derivative terms

The entropy of a BTZ black hole in the presence of gravitational Chern-Simons terms has previously been analyzed using Euclidean action formalism. In this paper we treat the BTZ solution as a two dimensional black hole by regarding the angular coordinate as a compact direction, and use Wald's Noether charge method to calculate the entropy of this black hole in the presence of higher derivative and gravitational Chern-Simons terms. The parameters labelling the black hole solution can be determined by extremizing an entropy function whose value at the extremum gives the entropy of the black hole.