Using the off-shell formulation for general N = 2 supergravity-matter systems developed in arXiv:0905.0063, we propose a construction to generate a restricted chiral superfield from any real weight-zero projective multiplet L. One can choose L to be composed of tensor multiplets, O(2n) multiplets, with n=2,3,..., and polar hypermultiplets. In conjunction with the standard procedure to induce a N = 2 linear multiplet from any chiral weight-one scalar, we obtain a powerful mechanism to generate higher-derivative couplings in supergravity. In the case that L is a homogeneous function of n tensor multiplets of degree zero, we show that our construction is equivalent to that developed by de Wit and Saueressig in arXiv:hep-th/0606148 using the component superconformal tensor calculus. We also work out nontrivial examples with L composed of O(2n)and tensor multiplets.
In this paper, we use the superconformal approach to derive the higher derivative action for N = 3 Poincare supergravity in four space-time dimensions. We first study the coupling of N = 3 vector multiplets to conformal supergravity. Thereafter we combine it with the pure N = 3 conformal supergravity action and use a minimum of three vector multiplets as compensators to arrive at Poincare supergravity with higher derivative corrections. We give a general prescription on how to eliminate the auxiliary fields in an iterative manner and obtain the supergravity action order by order in derivatives…
We study four-derivative corrections to pure $\mathcal{N}=2$, $D=5$ gauged supergravity. In particular, we find that, up to field redefinitions, there is a single four-derivative superinvariant that one can add to the action, up to factors of the two-derivative action. Consequently, this selects out a unique set of coefficients for the four-derivative corrections. We confirm these coefficients (in the ungauged limit) on the BMPV solution.
We study four-derivative corrections to 5d $\mathcal{N}=2$ minimal gauged supergravity using tools from conformal supergravity. There are two supersymmetric invariants at the four-derivative order and we show explicitly how to write down the action in the Poincaré frame in terms of their coefficients. We apply our results in the context of holography where the four-derivative terms in the supergravity action translate into corrections to the conformal anomalies of the dual 4d $\mathcal{N}=1$ SCFT. We use these results to study corrections to the entropy of the supersymmetric black string solut…
We study the vacuum structures of four-dimensional $\mathcal{N} = 1$ 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.
We use conformal supergravity techniques to study four-derivative corrections in four-dimensional gauged supergravity. We show that the four-derivative Lagrangian for the propagating degrees of freedom of the $\mathcal{N}=2$ gravity multiplet is determined by two real dimensionless constants. We demonstrate that all solutions of the two-derivative equations of motion in the supergravity theory also solve the four-derivative equations of motion. These results are then applied to explicitly calculate the regularized on-shell action for any asymptotically locally AdS$_4$ solution of the two-deriv…
An action for the higher-derivative corrections to minimal gauged supergravity in four dimensions has been recently proposed. We demonstrate that the supersymmetric solutions of this model are those of the two-derivative action, and investigate some of their properties. In particular, we prove a formula for the renormalised on-shell action in terms of contributions from fixed points of a $U(1)$ action, and confirm that it is invariant under deformations which preserve the boundary almost contact structure.
We construct the first rotating string solution in 6-dimensional Einstein-Gauss-Bonnet supergravity, carrying both electric and magnetic charges. By embedding the known rotating string solution of the 2-derivative theory into 6-dimensional off-shell supergravity, the Killing spinors associated with the underlying supersymmetry can be made off-shell and are universal to all off-shell supergravity models based on the same field content. The near-horizon geometry is S^3 fibred over the extremal BTZ black hole, locally isomorphic to AdS_3*S^3. We compute the higher-derivative corrections to the Br…
We will use the covariant superform approach to develop a new density formula for $\mathcal{N}=2$ conformal supergravity which is based on a fermionic multiplet whose lowest component is a dimension-5/2 spinor. We will show that this density formula admits an embedding of the real scalar multiplet of [arXiv:1712.02309]. Upon using the embedding of the tensor multiplet into the real scalar multiplet, we will construct a new higher derivative action of the tensor multiplet in $\mathcal{N}=2$ conformal supergravity.
We study four-derivative corrections to four-dimensional $\mathcal{N}=2$ minimal gauged supergravity and show that they are controlled by two real constants. The solutions of the equations of motion in the two-derivative theory are not modified by the higher-derivative corrections. We use this to derive a general formula for the regularized on-shell action for any asymptotically locally AdS$_4$ solution of the theory and show how the higher-derivative corrections affect black hole thermodynamic quantities in a universal way. We employ our results in the context of holography to derive explicit…
We analyze BPS black hole attractors in 4d gauged supergravity in the presence of higher derivative supersymmetric terms, including a Weyl-squared-type action, and determine the resulting corrections to the Bekenstein-Hawking entropy. The near-horizon geometry AdS$_2 \times$S$^2$ (or other Riemann surface) preserves half of the supercharges in $N=2$ supergravity with Fayet-Iliopoulos gauging. We derive a relation between the entropy and the black hole charges that suggests via AdS/CFT how subleading corrections contribute to the supersymmetric index in the dual microscopic picture. Depending o…
Spectrum of Higher Derivative 6D Chiral Supergravity
具有N=（1，0）超对称性的六维规范离壳麦克斯韦-爱因斯坦超引力具有由超对称化黎曼平方项提供的高阶导数延拓。这个理论允许一个超对称Minkowski x S^2紧化，在S^2上有一个单位电荷的U（1）π。我们确定在此背景下的理论的全谱。我们还确定了这种紧化的非超对称形式的谱，在这种紧化中，π荷不同于1，我们发现了一个奇特的特征，即在由π荷确定的S^2等距群的表示中存在无质量的引力子。
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 $T^4$ is followed by a consistent truncation. In the resulting action the hyperscalar fields parametrize the coset $SO(4,4)/(SO(4)\times SO(4))$. 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 r…
BMPV black holes in higher-derivative supergravity
Leinweber Institute for Theoretical Physics, University of Michigan（密歇根大学莱恩韦伯理论物理研究所）；Tianjin University（天津大学）；Peng Huanwu Center for Fundamental Theory（彭桓武基础理论中心）
BPS Solutions of 4d Euclidean N=2 Supergravity with Higher Derivative Interactions
Sogang University（西江大学）；Indian Institute of Science Education and Research Thiruvananthapuram（印度科学教育研究所特里凡得琅分校）；Chennai Mathematical Institute（金奈数学研究所）
We use 4d ambitwistor string theory to derive new worldsheet formulae for tree-level conformal supergravity amplitudes supported on refined scattering equations. Unlike the worldsheet formulae for super-Yang-Mills or supergravity, the scattering equations for conformal supergravity are not in general refined by MHV degree. Nevertheless, we obtain a concise worldsheet formula for any number of scalars and gravitons which we lift to a manifestly supersymmetric formula using four types of vertex operators. The theory also contains states with non-plane wave boundary conditions and we show that th…
We study the cosmological evolution of a N = 1 supergravity model, dual to a higher derivative supergravity model coupled to scalar fields so that in the Einstein frame the model is ghost free. We find that this model admit slow roll inflationary solutions showing essentially two-field inflation. The cosmological parameters calculated for this model lie in acceptable range with corrections of the order lnN/N, N being the number of e-foldings, compared to the Starobinsky inflation model.
Within the framework of six-dimensional ${\cal N}=(1,0)$ conformal supergravity, we introduce new off-shell multiplets ${\cal O}{}^{*}(n)$, where $n=3,4,\dots,$ and use them to construct higher-rank extensions of the linear multiplet action. The ${\cal O}{}^{*}(n)$ multiplets may be viewed as being dual to well-known superconformal ${\cal O}(n)$ multiplets. We provide prepotential formulations for the ${\cal O}(n)$ and ${\cal O}{}^{*}(n)$ multiplets coupled to conformal supergravity. For every ${\cal O}{}^{*}(n)$ multiplet, we construct a higher derivative invariant which is superconformal on …
We develop computational tools for calculating supersymmetric higher-order derivative corrections to eleven-dimensional supergravity using the action principle approach. We show that, provided the superspace Bianchi identities admit a perturbative solution in the derivative expansion, there are at least two independent superinvariants at the eight-derivative order of eleven-dimensional supergravity. Assuming the twelve-superforms associated to certain anomalous Chern-Simons terms are Weil-trivial, there will be a third independent superinvariant at this order. Under certain conditions, at leas…
We study four-derivative corrections to five-dimensional minimal gauged supergravity. We evaluate the on-shell action of the AdS$_5$ black hole solution with two independent angular momenta and one electric charge at linear order in the corrections. After imposing supersymmetry, we are able to recast the action in terms of the supersymmetric chemical potentials and match the result obtained from the dual superconformal index on the second sheet. To achieve this, we exploit the freedom to implement field redefinitions to recast the action in a much simpler form, as well as the fact that the two…
We initiate a systematic study of supersymmetric backgrounds in 4d $\mathcal{N}=2$ Euclidean supergravity in the presence of infinite towers of higher derivative corrections. Adopting a Gibbons-Hawking view towards the evaluation of the action in terms of nuts and bolts, we consider the two maximally symmetric vacua $\mathbb{R}^4$ and $\mathbb{H}^4$ (Euclidean AdS$_4$) and their unique supersymmetric deformations with (anti-) self-dual Maxwell tensors corresponding to a single nut at the center. These are the Omega background of Nekrasov-Okounkov, $Ω\, \mathbb{R}^4$, and its generalization wit…
We perform a Kaluza-Klein reduction of IIB supergravity including purely gravitational $α'^3$-corrections on a Calabi-Yau threefold, and perform the orientifold projection accounting for the presence of $O3/O7$-planes. We consider infinitesimal Kähler deformations of the Calabi-Yau background and derive the complete set of four-derivative couplings quadratic in these fluctuations coupled to gravity. In particular, we find four-derivative couplings of the Kähler moduli fields in the four-dimensional effective supergravity theory, which are referred to as friction couplings in the context of inf…
We study the interplay between four-derivative 4d gauged supergravity, holography, wrapped M5-branes, and theories of class $\mathcal{R}$. Using results from Chern-Simons theory on hyperbolic three-manifolds and the 3d-3d correspondence we are able to constrain the two independent coefficients in the four-derivative supergravity Lagrangian. This in turn allows us to calculate the subleading terms in the large-$N$ expansion of supersymmetric partition functions for an infinite class of three-dimensional $\mathcal{N}=2$ SCFTs of class $\mathcal{R}$. We also determine the leading correction to th…
