Martin Cederwall
We provide a linearised superfield description of the exotic non-metric $N=(4,0)$ supergravity in $D=6$, by using a pure spinor superfield formalism. The basic field $Ψ$ is a ghost number 2 scalar, transforming in the same R-symmetry module as the tensor fields. Partial results for the $N=(3,1)$ model are presented.
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Compactifications of Type II Supergravities in Superspace
本文提出利用纯旋量超弦自然给出的超空间，直接描述带通量 II 型超引力紧化，并证明其可重现已有结果。
The N-extended supersymmetric self-dual Poincaré supergravity equations provide a natural local description of supermanifolds possessing hyperkähler structure. These equations admit an economical formulation in chiral superspace. A reformulation in harmonic superspace encodes self-dual supervielbeins and superconnections in a graded skew-symmetric supermatrix superfield prepotential satisfying generalised Cauchy-Riemann conditions. A recipe is presented for extracting explicit self-dual supervielbeins and superconnections from such `analytic' prepotentials. We demonstrate the method by explici…
We analyze actions for 2D supergravities induced by chiral conformal supermatter. The latter may be thought as described at the classical level by superspace actions invariant under super-reparametrization, super-Weyl and super-Lorentz transformations. Upon quantization various anomalies appear which characterize the non-trivial induced actions for the supergravitational sector. We derive these induced actions using a chiral boson to represent the chiral inducing matter. We show that they can be defined in a super-reparametrization invariant way, but with super-Weyl and super-Lorentz anomalies…
We review some recent results on the construction in superspace of 3D N=2 AdS supergravities and on the formulation of rigid supersymmetric theories in (1,1) and (2,0) AdS superspaces.
Basics of ${\cal N}=2, 4D$ conformal and Einstein supergravities in the harmonic superspace approach are outlined. The crucial merit of this formulation consists in that the relevant off-shell supermultiplets, in particular ${\cal N}=2, 4D$ superconformal Weyl multiplet, are accommodated by the harmonic-analytic unconstrained prepotentials with a clear geometric meaning, like in the analogous formulation of ${\cal N}=2, 4D$ supersymmetric gauge theory. The fundamental gauge group of conformal supergravity is constituted by the analyticity-preserving diffeomorphisms of harmonic superspace. The …
We investigate exotic supergravity theories in 6D with maximal (4,0) and (3,1) supersymmetry, which were conjectured by C. Hull to exist and to describe strong coupling limits of ${\cal N}=8$ theories in 5D. These theories involve exotic gauge fields with non-standard Young tableaux representations, subject to (self-)duality constraints. We give novel actions in a 5+1 split of coordinates whose field equations reproduce those of the free bosonic (4,0) and (3,1) theory, respectively, including the (self-)duality relations. Evidence is presented for a master exceptional field theory formulation …
We perform a systematic search for all possible massive deformations of IIA supergravity in ten dimensions. We show that there exist exactly two possibilities: Romans supergravity and Howe-Lambert-West supergravity. Along the way we give the full details of the ten-dimensional superspace formulation of the latter. The scalar superfield at canonical mass dimension zero (whose lowest component is the dilaton), present in both Romans and massless IIA supergravities, is not introduced from the outset but its existence follows from a certain integrability condition implied by the Bianchi identities…
We first review standard results of the compactification of type IIA and IIB supergravities on a Calabi-Yau threefold and illustrate mirror symmetry. Then we compactify the same theories on a class of generalized Calabi-Yau manifolds called Half-flat. We obtain the scalar potential, and we show that type IIA on a Half-flat manifold is mirror symmetric to type IIB on a Calabi-Yau threefold with electric NS-fluxes turned on. In the last part, we compute the full equations of motion for N=4 supergravity in central charge superspace with the graviphotons identified as central charge components of …
For general off-shell N=2 supergravity-matter systems in three spacetime dimensions, a formalism is developed to reduce the corresponding actions from superspace to components. The component actions are explicitly computed in the cases of Type I and Type II minimal supergravity formulations. We describe the models for topologically massive supergravity which correspond to all the known off-shell formulations for three-dimensional N=2 supergravity. We also present a universal setting to construct supersymmetric backgrounds associated with these off-shell supergravities.
The equations of motion (e.m.'s) of the N=1, D=10 anomaly free supergravity, obtained in the framework of the superspace approach, are analyzed. The formal equivalence of the usual and dual supergravities is discussed at the level of e.m.'s. The great simplicity of the dual formulation is established. The possibillity of the lagrangian formulation of the dual supergravity is pointed out. The bosonic part of the lagrangian is constructed including anomaly compensating superstring corrections.
Exotic supergravities and the Swampland
本研究针对六维奇异超引力与沼泽地猜想的相容性展开，证明(4,0)理论因紧致化后存在整体对称性与沼泽地无整体对称性猜想矛盾，指出仅(3,1)理论满足约化为爱因斯坦引力且无整体对称性的条件。
We describe new $N$-extended 2D supergravities on a $(p+1)$-dimensional (bosonic) space. The fundamental objects are moving frame densities that equip each $(p+1)$-dimensional point with a 2D ``tangent space''. The theory is presented in a $[p+1, 2]$ superspace. For the special case of $p=1$ we recover the 2D supergravities in an unusual form. The formalism has been developed with applications to the string-parton picture of $D$-branes at strong coupling in mind.
String and M-theory contain a family of branes forming U-duality multiplets. In particular, standard branes with codimension higher than or equal to two, can be explicitly found as supergravity solutions. However, whether domain-wall branes and space-filling branes can be found as supergravity solutions is still unclear. In this paper, we firstly provide a full list of exotic branes in type II string theory or M-theory compactified to three or higher dimensions. We show how to systematically obtain backgrounds of exotic domain-wall branes and space-filling branes as solutions of the double fie…
We present the superfield generalization of free higher spin equations in tensorial superspaces and analyze tensorial supergravities with GL(n) and SL(n) holonomy as a possible framework for the construction of a non-linear higher spin field theory. Surprisingly enough, we find that the most general solution of the supergravity constraints is given by a class of superconformally flat and OSp(1|n)-related geometries. Because of the conformal symmetry of the supergravity constraints and of the higher spin field equations such geometries turn out to be trivial in the sense that they cannot genera…
We compute the form of the Lagrangian of N=1 supersymmetric theories with gauged axion symmetries. It turns out that there appear generalized Chern-Simons terms that were not considered in previous superspace formulations of general N=1 theories. Such gaugings appear in supergravities arising from flux compactifications of superstrings, as well as from Scherk-Schwarz generalized dimensional reduction in M-theory. We also present the dual superspace formulation where axion chiral multiplets are dualized into linear multiplets.
We use the superspace formulation of supergravity in eleven and ten dimensions to compute fermion couplings on the M2-brane and on D$p$-branes. In this formulation fermionic couplings arise naturally from the $θ$-expansion of the superfields from which the brane actions are constructed. The techniques we use and develop can in principle be applied to determine the fermionic couplings to general background fields up to arbitrary order. Starting with the superspace formulation of 11-dimensional supergravity, we use a geometric technique known as the `normal coordinate' method to obtain the $θ$-e…
We perform a systematic search for static solutions in different sectors of 5d $N=8$ supergravities with compact and non-compact gauged R-symmetry groups, finding new and listing already known backgrounds. Due to the variety of possible gauge groups and resulting scalar potentials, the maximally symmetric vacua we encounter in these theories can be Minkowski, de Sitter, or anti-de Sitter. There exist BPS and non-BPS near-horizon geometries and full solutions with all these three types of asymptotics, corresponding to black holes, branes, strings, rings, and other black objects with more exotic…
We discuss the dynamics of a superparticle in a superspace whose isometry is generated by the superalgebra OSp(1|4) or its central-charge contraction. Extra coordinates of the superspace associated with tensorial central charges are shown to describe spin degrees of freedom of the superparticle, so quantum states form an infinite tower of (half)-integer helicities. A peculiar feature of the model is that it admits BPS states which preserve 3/4 of target-space supersymmetries.
The quest for unification of particles and fields and for reconciliation of Quantum Mechanics and General Relativity has led us to gauge theories, string theories, supersymmetry and higher-extended objects: membranes... Our spacetime is quantum mechanical but it admits semiclassical descriptions of various ``complementary'' kinds that could be valid approximations in various circumstances. One of them might be supergravity in 11 dimensions the largest known interacting theory of a finite number of fields with gauged Poincar\' e supersymmetry. Its solitons and their dual membranes would be stat…
We present expressions for the supercurrents generated by a generic $4D,~\mathcal{N}=1$ theory of complex linear superfield $Σ$. We verify that these expressions satisfy the appropriate superspace conservation equations. Furthermore, we discuss the component projection in order to derive expressions for the energy-momentum tensor, the supersymmetry current and the R-symmetry current when available. In addition, we discuss aspects of the coupling of the theory to supergravity. Specifically, we present a straightforward method to select the appropriate formulations of supergravity that one must …
The $N=2$ supersymmetric {\it self-dual} Yang-Mills theory and the $N=4$ and $N=2$ {\it self-dual} supergravities in $2+2$ space-time dimensions are formulated for the first time. These formulations utilize solutions of the Bianchi identities subject to the super-Yang-Mills or supergravity constraints in the relevant $N$-extended superspace with the space-time signature $(2,2)$.
We obtain a four-dimensional supergravity with spontaneously broken supersymmetry allowing for de Sitter vacua by coupling a superspace action of minimal N=1, D=4 supergravity to a locally supersymmetric generalization of the Volkov-Akulov goldstino action describing the dynamics of a space-filling non-BPS 3-brane in N=1, D=4 superspace. To the quadratic order in the goldstino field the obtained action coincides with earlier constructions of supergravities with nilpotent superfields, while matching the higher-order contributions will require a non-linear redefinition of fields. In the unitary …
Higher Derivative Supergravities in Diverse Dimensions
本文综述 $1\le D\le 11$ 维在壳与离壳高导数超引力的构造方法、玻色不变量、费米子超变换、在壳化、超对称解及对偶对称性作用。
Exotic gravity theory in loop space
本文在圈空间中研究了C. Hull提出的D=6, (4,0)超空间奇异线性化超共形引力理论，证明其玻色子部分的引力势C和曲率G可重新解释为圈空间上的超局部线性化度规和曲率。
Exotic gravity theory in topologically non-trivial spacetimes
本文探讨了 Hull 提出的六维超共形引力理论在拓扑非平凡时空中的玻色子扇区，将其视为 $H=dB$ 理论的平方，并简要涉及十一维超引力的形式扇区。
Quantum planes which correspond to all one parameter solutions of QYBE for the two-dimensional case of GL-groups are summarized and their geometrical interpretations are given. It is shown that the quantum dual plane is associated with an exotic solution of QYBE and the well-known quantum $h$-plane may be regarded as the quantum analog of the flag (or fiber) plane. Contractions of the quantum supergroup $ GL_q(1|2)$ and corresponding quantum superspace $ C_q(1|2)$ are considered in Cartesian basis. The contracted quantum superspace $ C_h(1|2;ι)$ is interpreted as the non-commutative analog of …
New aspects of the Z$_{\textrm 2}$ $\times$ Z$_{\textrm 2}$-graded 1D superspace: induced strings and 2D relativistic models
本文将Z₂×Z₂阶化超空间中的奇异玻色坐标与其他坐标同等处理，诱导出新的二维相对论超庞加莱模型和紧化闭弦，并得到非简并的β变形点粒子模型。
We present a flux formulation of Double Field Theory, in which geometric and non-geometric fluxes are dynamical and field-dependent. Gauge consistency imposes a set of quadratic constraints on the dynamical fluxes, which can be solved by truly double configurations. The constraints are related to generalized Bianchi Identities for (non-)geometric fluxes in the double space, sourced by (exotic) branes. Following previous constructions, we then obtain generalized connections, torsion and curvatures compatible with the consistency conditions. The strong constraint-violating terms needed to make c…
Extended field theories (ExFTs) are a relatively young class of theories that lie at the intersection of Kaluza-Klein theory and the remarkable dualities of string- and M-theory. Whereas the original Kaluza-Klein construction unified the local symmetries of an Einstein-Maxwell-dilaton theory into diffeomorphisms in one dimension higher, ExFTs aim for a much more ambitious goal: to unify the local symmetries of supergravity fields into a single symmetry manifest on a higher-dimensional space. Depending on whether we start with Type II or 11-dimensional supergravity, we obtain double and excepti…
The Geometry, Branes and Applications of Exceptional Field Theory
本文综述了例外场论，该理论通过扩展几何统一超引力度规与p-形式场，将隐藏的例外李对称性几何化，从而简化对偶轨道并用于研究M-理论中的奇异膜与非几何结构。
Non-compact gauge groups, tensor fields and Yang-Mills-Einstein amplitudes
本文为具有非紧致规范群的五维N=2超引力构造双拷贝构建，利用超Yang-Mills和Yang-Mills-标量理论的振幅，并扩展到有质量自对偶张量，展示了Heisenberg群的出现及可能的奇异张量-矢量耦合。
This thesis is devoted to various aspects of electric-magnetic duality and its gravitational generalization, with an emphasis on the case of maximal supergravity. It is divided into three parts. In the first part, we review the the Cremmer-Julia "hidden" symmetries of maximal supergravity in various dimensions. Two new results are obtained: we prove that those symmetries appear if and only if the Chern-Simons coupling of the $D=11$ theory takes the value predicted by supersymmetry, and we obtain a manifestly $E_{7(7)}$-invariant formula for the entropy of non-extremal black holes in $D=4$, $N=…
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