Presence Of Higher Derivative Terms Research Articles

Action complexity of charged black holes with higher derivative interactions

Quantum complexity of CFT states can be computed holographically from the dual gravitational solutions. In this paper, we have studied the late time growth of holographic complexity of a charged black hole in five-dimensional, Anti-de Sitter spacetime in the presence of quartic derivative interaction terms using the Complexity = Action conjecture. These interaction terms in the gravitational action can lead to the violation of Llyod's bound. The dual CFT is known to admit a hydrodynamic description where the KSS bound is also violated due to the presence of higher derivative terms in the bulk action. The origin of terms which violate both the bounds are the same for the gravitational action of consideration. We have also discussed the late time complexity growth rate of the Jackiw-Teitelboim (JT) model with higher derivative corrections.

Page curves of Reissner–Nordström black hole in HD gravity

We obtain the Page curves of an eternal Reissner–Nordström black hole in the presence of higher derivative terms in four dimensions. We consider two cases: gravitational action with general {mathcal {O}}(R^2) terms plus Maxwell term and Einstein–Gauss–Bonnet gravity plus Maxwell term. In both the cases entanglement entropy of the Hawking radiation in the absence of island surface is increasing linearly with time. After including contribution from the island surface, we find that after the Page time, entanglement entropy of the Hawking radiation in both the cases reaches a constant value which is the twice of the Bekenstein–Hawking entropy of the black hole and we obtain the Page curves. We find that Page curves appear at later or earlier time when the Gauss–Bonnet coupling increases or decreases. Further, scrambling time of Reissner–Nordström is increasing or decreasing depending upon whether the correction term (coming from {mathcal {O}}(R^2) terms in the gravitational action) is increasing or decreasing in the first case whereas scrambling time remains unaffected in the second case (Einstein–Gauss–Bonnet gravity case). As a consistency check, in the limit of vanishing GB coupling we obtain the Page curve of the Reissner–Nordström black hole obtained in Wang et al. (JHEP 04:103, 2021).

Island in the presence of higher derivative terms

Using extended island formula we compute entanglement entropy of Hawking radiation for black hole solutions of certain gravitational models containing higher derivative terms. To be concrete we consider two different four dimensional models to compute entropy for both asymptotically flat and AdS black holes. One observes that the resultant entropy follows the Page curve, thanks to the contribution of the island, despite the fact that the corresponding gravitational models might be non-unitary.

AdS/BCFT correspondence, holographic g-theorem and Gauss–Bonnet gravity

We investigate some aspects of holographic dual of boundary conformal field theories for higher derivative Gauss–Bonnet (GB) gravity. We explore the holographic g-theorem for GB gravity and introduce holographic g-functions in five and six dimensions. Focusing on the coefficients of the logarithmic terms in the partition functions of BCFTs holographically, and in the presence of higher derivative terms, in even dimensions we show that these are associated with corrected A-type trace anomaly. Building on this, in odd dimensions, we present supporting evidence for monotonicity property of boundary central charge in BCFT5 in Einstein gravity. However, in the GB gravity case, we find that the monotonicity behavior is violated. This invalidates the holographic g-theorem for the GB gravity.

Higher Derivative Corrections to Non-Abelian Vortex Effective Theory

We give a systematic method to calculate higher derivative corrections to low-energy effective theories of solitons, which are in general non-linear sigma models on the moduli spaces of the solitons. By applying it to the effective theory of a single BPS non-Abelian vortex in U(N) gauge theory with N fundamental Higgs fields, we obtain four derivative corrections to the effective sigma model on the moduli space C \times CP^{N-1}. We compare them with the Nambu-Goto action and the Faddeev-Skyrme model. We also show that Yang-Mills instantons/monopoles trapped inside a non-Abelian vortex membrane/string are not modified in the presence of higher derivative terms.

Near-horizon analysis of [formula omitted

It is now well understood that the coefficient of shear viscosity of boundary fluid can be obtained from the horizon values of the effective coupling of transverse graviton in bulk spacetime. In this paper we observe that to find the shear-viscosity coefficient it is sufficient to know only the near-horizon geometry of the black hole spacetime. One does not need to know the full analytic solution. We consider several examples including non-trivial matter (dilaton, gauge fields) coupled to gravity in presence of higher derivative terms and calculate shear viscosity for both extremal and non-extremal black holes only studying the near-horizon geometry. In particular, we consider higher derivative corrections to extremal R-charged black holes and compute η / s in presence of three independent charges. We also consider asymptotically Lifshitz spacetime whose dual black hole geometry cannot be found analytically. We study the near horizon behaviour of these black holes and find η / s for its dual plasma at Lifshitz fixed point.

DEVELOPMENT OF A HIGHER-ORDER ACCURATE RECONSTRUCTION SCHEME WITH REDUCED LEAST SQUARE MATRIX FOR CONVECTIVE AND DIFFUSIVE FLUX EVALUATION

The development of a higher-order reconstruction scheme with reduced least square matrix is presented. The matrix used in conventional least square based reconstruction schemes for finite volume solvers contains bigger terms. For solution dependent schemes, this matrix has to be inverted for each time step, which is computationally costlier. To overcome this, certain mathematical principles applicable to finite volume formulation, have been used to eliminate a good number of terms appearing in the matrix. In addition, accurate and computationally efficient derivative plug-ins are incorporated to make the formulation generalized so that one can extend it to any order of accuracy. The presence of higher derivative terms in this scheme ensures uniformly higher-order accuracy throughout the flow domain. The reduced matrix can be used for data independent as well as solution dependent reconstruction schemes. Computationally efficient stencil searching algorithm, satisfying physical and topological requirements and capable of handling structured, unstructured, and adaptive grids has been coupled with the scheme. The scheme has been successfully used to simulate flow over blunt cone-flare, NASA B2 nozzle, and high altitude test facility. The solver has shown around 30% saving in least square matrix evaluation time.

Higher derivative correction to Kaluza–Klein black hole solution

We investigate the attractor mechanism in a Kaluza–Klein black hole solution in the presence of higher derivative terms. In particular, we discuss the attractor behavior of static black holes by using the effective potential approach as well as the entropy function formalism. We consider different higher derivative terms with a general coupling to the moduli field. For the R 2 theory, we use an effective potential approach, looking for solutions which are analytic near the horizon and showing that they exist and enjoy attractor behavior. The attractor point is determined by extremization of the modified effective potential at the horizon. We study the effect of the general higher derivative corrections of R n terms. Using the entropy function we define the modified effective potential and we find the conditions to have the attractor solution. In particular for a single charged Kaluza–Klein black hole solution we show that a higher derivative correction dresses the singularity for an appropriate coupling, and we can find the attractor solution.

Moduli flow and non-supersymmetric AdS attractors

We investigate the attractor mechanism in gauged supergravity in the presence of higher derivative terms. In particular, we discuss the attractor behavior of static black hole horizons in anti-de Sitter spacetime by using the effective potential approach as well as Sen's entropy function formalism. We use the holographic techniques to interpret the moduli flow as an RG flow towards the IR attractor horizon. We find that the holographic c-function obeys the expected properties and point out some subtleties in understanding attractors in AdS.

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.

OnR2corrections for 5D black holes

We study higher order corrections to the entropy of extremal BPS black holes/string in five dimensions. These corrections are due to supersymmetric completion of R2 terms. These results can be used to make a connection between total bundle space of near horizon wrapped M2's and wrapped M5's in the presence of higher derivative terms. We also show how the corrected geometry removes the singularity of a small black hole.

5D black holes and strings with higher derivatives

We find asymptotically flat black hole and string solutions to 5D supergravity in the presence of higher derivative terms. In some cases, including the fundamental heterotic string solution, the higher derivative terms smooth out naked singularities into regular geometries carrying zero entropy. We also compute corrections to the entropy of 5D Calabi-Yau black holes, and discuss the relation to previous results.

Anisotropic higher derivative gravity and inflationary universe

Stability analysis of the Kantowski-Sachs type universe in pure higher derivative gravity theory is studied in details. The non-redundant generalized Friedmann equation of the system is derived by introducing a reduced one dimensional generalized KS type action. This method greatly reduces the labor in deriving field equations of any complicate models. Existence and stability of inflationary solution in the presence of higher derivative terms are also studied in details. Implications to the choice of physical theories are discussed in details in this paper.

How does a fundamental string stretch its horizon?

It has recently been shown that if we take into account a class of higher derivative corrections to the effective action of heterotic string theory, the entropy of the black hole solution representing elementary string states correctly reproduces the statistical entropy computed from the degeneracy of elementary string states. So far the form of the solution has been analyzed at distance scales large and small compared to the string scale. We analyze the solution that interpolates between these two limits and point out a subtlety in constructing such a solution due to the presence of higher derivative terms in the effective action. We also study the T-duality transformation rules to relate the moduli fields of the effective field theory to the physical compactification radius in the presence of higher derivative corrections and use these results to find the physical radius of compactification near the horizon of the black hole. The radius approaches a finite value even though the corresponding modulus field vanishes. Finally we discuss the non-leading contribution to the black hole entropy due to space-time quantum corrections to the effective action and the ambiguity involved in comparing this result to the statistical entropy.

Inflationary universe in higher derivative induced gravity

In an induced-gravity model, the stability condition of an inflationary slow-rollover solution is shown to be $\phi_0 \partial_{\phi_0}V(\phi_0)=4V(\phi_0)$. The presence of higher derivative terms will, however, act against the stability of this expanding solution unless further constraints on the field parameters are imposed. We find that these models will acquire a non-vanishing cosmological constant at the end of inflation. Some models are analyzed for their implication to the early universe.

QUANTUM GRAVITATIONAL EFFECTS AND THE COMPACTIFICATION SCALE IN THE HETEROTIC SUPERSTRING THEORY

It is known that quantum gravitational effects due to virtual black holes and wormholes can exert an important influence by violating global symmetries. These processes have recently been investigated by Kallosh et al., who found, for the heterotic superstring theory, that there is a sufficient suppression of deleterious effects via the Euclidean action S E from the presence of higher-derivative terms occurring as a topological invariant, the Euler characteristic χ, regardless of the precise details of the underlying wormhole solution. Here, we consider this result further, arguing, in the absence of inflation, that there are no large wormholes in the heterotic superstring theory for which the wormhole action per se is large enough, topological suppression being the only possibility. The model-independent superstring axion may be susceptible to these corrections, because, as shown by Witten, it possesses a non-linearly realized, global U(1) symmetry, being a real scalar field coupled to the anomalous term [Formula: see text] from the outset, and they are relevant to the R-parity symmetry. Allowing for the unknown effect of the black holes, however, we conjecture that these quantum gravitational effects produce no observable consequences.

Relativistic force and the anisotropy of mass

The quantization of nonrelativistic electromagnetic interaction of anyons when higher derivative terms are included in the Lagrangian is discussed. The gauge model U(1) U(1) under consideration, contains the statistical U(1) Chern-Simons field and the electromagnetic field, both coupled to a fractional spin matter field. A higher derivative term preserving gauge invariance is added and the new model obtained is studied in the framework of the generalized constrained Hamiltonian systems. Next, by extending the Faddeev±Senjanovic method to higher derivative systems, the path-integral quantization is developed and the diagrammatic and Feynman rules in the framework of the perturbative theory, are discussed. In this context, only a mixed bosonic propagator can be defined. As happens in other more simple models, and in this case, the addition of higher derivative terms improves the ultraviolet behaviour of some diagrams, rendering this renormalizable model less divergent. Finally, a possible way of solving the unitary problem due to the presence of higher derivative terms is proposed.