Higher Derivative Corrections Research Articles

Higher derivative corrections to black brane thermodynamics and the weak gravity conjecture

We study higher derivative corrections to black brane thermodynamics and their implications for the weak gravity conjecture for p-form gauge fields. In particular we show that higher derivative corrections decrease tension-to-charge ratios of extremal black branes as implied by the weak gravity conjecture, if four-derivative couplings follow scattering positivity bounds. We also demonstrate that entropy corrections in the micro canonical ensemble are positive under the same assumptions. This extends earlier works in the Einstein-Maxwell theory to p-form gauge fields in general spacetime dimensions.

Vacua by derivative corrections in mathcal {N} = 1 supergravity with matter multiplets

We study the vacuum structures of four-dimen-sional mathcal {N} = 1 old minimal supergravity with higher derivative corrections. We find that mathcal {N} = 1 supergravity with Riemann curvature square corrections and higher derivative matter chiral multiplets induces a non-trivial de Sitter vacuum, even in the absence of superpotentials. This vacuum generically breaks supersymmetry. We show that the auxiliary fields in the gravity and the chiral multiples play important roles to generate a potential in supersymmetric higher derivative theories.

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.

Black hole multipoles in higher-derivative gravity

We consider a broad family of higher-derivative extensions of four-dimensional Einstein gravity and study the multipole moments of rotating black holes therein. We carefully show that the various definitions of multipoles carry over from general relativity, and compute these multipoles for higher-derivative Kerr using the ACMC expansion formalism. We obtain the mass Mn and current Sn multipoles as a series expansions in the dimensionless spin; in some cases we are able to resum these series into closed-form expressions. Moreover, we observe the existence of intriguing relations between the corrections to the parity-odd multipoles S2n ≠ 0 and M2n+1 ≠ 0 that break equatorial symmetry, and the parity-preserving corrections that only modify S2n+1 and M2n. Further, we comment on the higher-derivative corrections to multipole ratios for Kerr, and we discuss the phenomenological implications of the corrections to the multipole moments for current and future gravitational wave experiments.

From rotating to charged black holes and back again

The mild form of the Weak Gravity Conjecture (WGC) requires higher derivative corrections to extremal charged black holes to increase their charge-to-mass ratio. This allows decay via emission of a smaller extremal black hole. In this paper, we investigate if similar constraints hold for extremal rotating black holes. We do so by considering the leading higher derivative corrections to the four-dimensional Kerr black hole and five-dimensional Myers-Perry black hole. We use a known mapping of these rotating solutions to a four-dimensional non-rotating dyonic Kaluza-Klein black hole and impose the WGC on this charged solution. Going back again to the rotating solutions, this fixes the sign of the corrections to the rotating extremality bounds. The sign of the corrections is non-universal, depending on the black hole under consideration. We argue that this is not at odds with black hole decay, because of the presence of a superradiant instability that persists in the extremal limit. When this instability is present, the WGC is implied for the four-dimensional charged black hole.

T duality and hints of generalized geometry in string α′ corrections

We examine the structure of higher-derivative string corrections under a cosmological reduction and make connection to generalized geometry and T-duality. We observe that, while the curvature $R^\mu{}_{\nu\rho\sigma}(\Omega_+)$ of the generalized connection with torsion, $\Omega_+=\Omega+\frac{1}{2}H$, is an important component in forming T-duality invariants, it is necessarily incomplete by itself. We revisit the tree-level $\alpha'R^2$ corrections to the bosonic and heterotic string in the language of generalized geometry and explicitly demonstrate that additional $H$-field couplings are needed to restore T-duality invariance. We also comment on the structure of the T-duality completion of tree-level $\alpha'^3R^4$ in the type II string.

Well-posed formulation of Einstein-Maxwell effective field theory

We consider the well-posedness of the initial value problem for Einstein-Maxwell theory modified by higher derivative effective field theory corrections. Field redefinitions can be used to bring the leading parity-symmetric 4-derivative corrections to a form which gives second order equations of motion. We show that a recently introduced "modified harmonic" gauge condition can be used to obtain a formulation of these theories which admits a well-posed initial value problem when the higher derivative corrections to the equations of motion are small.

ABJM at finite N via 4d supergravity

We apply the conjecture of [1] for gravitational building blocks to the effective supergravity description of M-theory on S7/ℤk. Utilizing known localization results for the holographically dual ABJM theory, we determine a complete tower of higher derivative corrections to the AdS4 supergravity and a further set of quantum corrections. This uniquely fixes the gravitational block, leading to holographic predictions for a number of exact ABJM observables, excluding only constant and non-perturbative corrections in the gauge group rank N. The predicted S3 partition function is an Airy function that reproduces previous results and generalizes them to include arbitrary squashing and mass deformations/R-charge assignments. The topologically twisted and superconformal indices are instead products of two different Airy functions, in agreement with direct numeric calculations in the unrefined limit of the former object. The general fixed-point formula for an arbitrary supersymmetric background is similarly given as a product of Airy functions.

The correlation of WGC and hydrodynamics bound with R4 correction in the charged AdS[formula omitted] black brane

This paper focuses on the possible correlation between conjectures KSS bound and weak gravity conjecture (WGC). The hydrodynamic values KSS bound and weak gravity conjecture constraint the low-energy effective field theory. These conjectures identify UV complete theories. We give four, six, and eight order derivative corrections to the corresponding action and employ the hyperscaling violating charged AdSd+2 black brane solution. These corrections lead us to find a correlation between conjectures KSS bound and weak gravity conjecture. We see that, with increasing perturbation correction, this correlation is more likely to appear. We consider dynamical constant z=1, d=5 and obtain the range of hyperscaling violation exponent d+z−2≤θ≤d+z−1 for the above mentioned black brane. Here, we show that higher derivative corrections reduce the ratio of MQ to extremal black holes. Likewise, we also obtain the universal relaxation bound τ≥1πT and KSS bound ηs≥14π for our model. The results indicate a possibility of a relationship between the two conjectures. Our studies also show the consistency of WGC and KSS bound conjectures for all corrections (except curvature-cubed, β2) in the extremal and near-extremal conditions.

Quantum entropy of BMPV black holes and the topological M-theory conjecture

We present a formula for the quantum entropy of supersymmetric five-dimensional spinning black holes in M-theory compactified on CY3, i.e., BMPV black holes. We use supersymmetric localization in the framework of off-shell five dimensional N = 2 supergravity coupled to I = 1, . , NV + 1 off-shell vector multiplets. The theory is governed at two-derivative level by the symmetric tensor {mathcal{C}}_{IJK} (the intersection numbers of the Calabi-Yau) and at four-derivative level by the gauge-gravitational Chern-Simons coupling cI (the second Chern class of the Calabi-Yau). The quantum entropy is an NV +2-dimensional integral parameterised by one real parameter φI for each vector multiplet and an additional parameter φ0 for the gravity multiplet. The integrand consists of an action governed completely by {mathcal{C}}_{IJK} and cI, and a one-loop determinant. Consistency with the on-shell logarithmic corrections to the entropy, the symmetries of the very special geometry of the moduli space, and an assumption of analyticity constrains the one-loop determinant up to a scale-independent function g(φ0). For g = 1 our result agrees completely with the topological M-theory conjecture of Dijkgraaf, Gukov, Neitzke, and Vafa for static black holes at two derivative level, and provides a natural extension to higher derivative corrections. For rotating BMPV black holes, our result differs from the DGNV conjecture at the level of the first quantum corrections.

Topology of black hole thermodynamics in Gauss-Bonnet gravity

Thermodynamics of black holes in anti de Sitter (AdS) spacetimes typically contains critical points in the phase diagram, some of which correspond to the first order transition ending in a second order one. Following the recent proposal in [arXiv:2112.01706] on using Duan's $\phi$-mapping theory, we classify the critical points of six dimensional charged Gauss-Bonnet black holes in AdS spacetime. We find that the higher derivative corrections from Gauss-Bonnet gravity do not change the topological class of critical points in charged black holes in AdS, unlike the case of Born-Infeld corrections noted earlier. The connection between the topological nature of critical points and existence of first order phase transitions breaks down in a certain parameter regime. A resolution is proposed by treating the novel and conventional critical points as phase creation and phase annihilation points, respectively. Examples are provided to support the proposal.

The seeds of EFT double copy

We explore the double copy of effective field theories (EFTs), in the recently proposed generalized color-kinematics and Kawai-Lewellen-Tye (KLT) approaches. In the former, we systematically construct scalar numerators satisfying the Jacobi identities from simpler numerator seeds with trace-like permutation properties. This construction has the advantage of being easily applicable to any multiplicity, which we exemplify up to 6-point. It employs the linear map between color factors formed by single traces of generators and by products of the structure constants, which also relates the generalized KLT and color-kinematics formalisms, allowing to produce KLT kernels at arbitrary order in the EFT expansion. At 4-point, we show that all EFT kernels are generated and that they only yield double-copy amplitudes which can also be obtained from the traditional KLT kernel. We perform initial checks suggesting that the same conclusions also hold at 5-point. We focus on single-trace massless scalar EFTs which however also control the higher-derivative corrections to gauge and gravity theories.

Higher-derivative corrections to black hole entropy at zero temperature

There is a well-established connection between the higher-derivative corrections to the black hole entropy and the black hole extremality bound. The particular combination of effective field theory (EFT) coefficients ${c}_{i}$ that controls the mass shift at fixed charge and temperature also controls the entropy shift at fixed charge and mass, in the limit where the mass approaches the uncorrected value for the extremal mass. In this paper, we use the classical entropy function formalism to examine the entropy corrections at exactly zero temperature, or at the corrected value for the extremal mass. We find that the zero-temperature entropy shift (a) is unrelated to the mass shift, (b) is $\mathcal{O}({c}_{i})$ in the EFT coefficients, rather than $\mathcal{O}(\sqrt{{c}_{i}})$, as is the constant-mass entropy shift, and (c) is negative in the example of the EFT arising at low energies from QED plus gravity.

Holographic evidence for nonsupersymmetric conformal manifolds

We provide the first holographic evidence for the existence of a nonsupersymmetric conformal manifold arising from exactly marginal but supersymmetry-breaking deformations of a superconformal three-dimensional field theory. In particular, we construct a 2-parameter nonsupersymmetric deformation of a supersymmetric AdS nongeometric background in type IIB string theory. We prove that the nonsupersymmetric backgrounds are perturbatively stable and also do not suffer from various nonperturbative instabilities. Finally, we argue that diffeomorphism symmetry protects our solutions against higher-derivative string corrections.

Corrections to extremal black holes from Iyer-Wald formalism

We present a general method of computing corrections to the extremality bound and entropy of Kerr-Newman black holes due to an arbitrary perturbation using the Iyer-Wald formalism. In this method, corrections to the extremality bound are given by an integral over an effective stress tensor which, in particular cases of interest, reduces to the usual stress tensor. This clarifies the relation between extremality corrections and energy conditions. In particular, we show that a necessary condition to decrease the mass of an extremal black hole in a canonical ensemble, as required by the weak gravity conjecture, is that the perturbation violates the dominant energy condition. As an application of our method, we compute higher-derivative corrections to charged black holes in anti-de Sitter space and Kerr black holes.

Higher-dimensional symmetry of AdS2×S2 correlators

It was recently shown that IIB supergravity on AdS5×S5 enjoys 10d conformal symmetry and that superstring theory on this background can be described using a 10d scalar effective field theory. In this paper we adapt these two complementary approaches to correlators of hypermultiplets in AdS2×S2. In particular, we show that 4-point correlators of 1/2-BPS operators in the 1d boundary can be computed using 4d conformal symmetry and a 4d effective action in the bulk. The 4d conformal symmetry is realised by acting with Casimirs of SU(1, 1|2), and is generically broken by higher derivative corrections. We point out similar structure underlying α′ corrections to IIB supergravity in AdS5×S5. In particular, while the α′3 corrections can be written in terms of a sixth order Casimir acting on a 10d conformal block, similar structure does not appear in higher-order corrections. We note however that a specific combination of higher derivative corrections can give rise to Witten diagrams with higher dimensional symmetry at the integrand level, with breaking then arising from the measure.

Generalizations of the double-copy: the KLT bootstrap

We formulate a new program to generalize the double-copy of tree amplitudes. The approach exploits the link between the identity element of the “KLT algebra” and the KLT kernel, and we demonstrate how this leads to a set of KLT bootstrap equations that the double-copy kernel has to satisfy in addition to locality constraints. We solve the KLT bootstrap equations perturbatively to find the most general higher-derivative corrections to the 4- and 5-point field theory KLT kernel. The new kernel generalizes the string KLT kernel and its associated monodromy relations. It admits new color-structures in the effective theories it double-copies. It provides distinct generalized KK and BCJ relations for the left and right single-color theories and is in that sense a ‘heterotic’-type double-copy. We illustrate the generalized double-copy in detail for 4d Yang-Mills theory with higher-derivative corrections that produce dilaton-axion-gravity with local operators up order ∇10R4. Finally, we initiate a search for new double-copy kernels.

Repulsive black holes and higher-derivatives

In two-derivative theories of gravity coupled to matter, charged black holes are self-attractive at large distances, with the force vanishing at zero temperature. However, in the presence of massless scalar fields and four-derivative corrections, zero-temperature black holes no longer need to obey the no-force condition. In this paper, we show how to calculate the long-range force between such black holes. We develop an efficient method for computing the higher-derivative corrections to the scalar charges when the theory has a shift symmetry, and compute the resulting force in a variety of examples. We find that higher-derivative corrected black holes may be self-attractive or self-repulsive, depending on the value of the Wilson coefficients and the VEVs of scalar moduli. Indeed, we find black hole solutions which are both superextremal and self-attractive. Furthermore, we present examples where no choice of higher-derivative coefficients allows for self-repulsive black hole states in all directions in charge space. This suggests that, unlike the Weak Gravity Conjecture, which may be satisfied by the black hole spectrum alone, the Repulsive Force Conjecture requires additional constraints on the spectrum of charged particles.

Dimensional reduction of higher derivative heterotic supergravity

Higher derivative couplings of hypermultiplets to 6D, N = (1, 0) supergravity are obtained from dimensional reduction of 10D heterotic supergravity that includes order α′ higher derivative corrections. Reduction on T4 is followed by a consistent truncation. In the resulting action the hyperscalar fields parametrize the coset SO(4, 4)/(SO(4) × SO(4)). While the SO(4, 4) symmetry is ensured by Sen’s construction based on string field theory, its emergence at the field theory level is a nontrivial phenomenon. A number of field redefinitions in the hypermultiplet sector are required to remove several terms that break the SO(4) × SO(4) down to its SO(4) diagonal subgroup in the action and the supersymmetry transformation rules. Working with the Lorentz Chern-Simons term modified 3-form field strength, where the spin connection has the 3-form field strength as torsion, is shown to simplify considerably the dimensional reduction.

String gravity in D=4

We revisit the four-dimensional theory of gravity that arises from string theory with higher-derivative corrections. By compactifying and truncating the ten-dimensional effective action of heterotic string theory at first order in $\alpha'$, and carefully dealing with field redefinitions, we show that the four-dimensional theory takes the form of an axidilaton model where the scalars couple to the Gauss-Bonnet and Pontryagin densities. Thus, the actual string gravity is a generalization of the well-studied Einstein-dilaton-Gauss-Bonnet and dynamical Chern-Simons models. Using this action we compute the stringy corrections to the Kerr geometry and we obtain, for the first time, the corrections to the entropy of the Kerr black hole at order $\alpha'^2$. We check that the first law of black hole mechanics is satisfied and discuss several properties of the solution. Our results suggest that there exist black hole solutions with $J>M^2$ and therefore the extremal ratio $J/M^2$ must be modified positively.