We find a curious duality between the bosonic sector of heterotic supergravity and the noncritical bosonic string with conformal anomaly. This allows us to map the Mink$_4\times S^3\times S^3$ vacuum of the bosonic string to a new warped $\mathbb R\times (T^{1,1}\times$Mink$_4)$ vacuum of the heterotic theory, which turns out to be supersymmetric, preserving $1/4$ of the supersymmetry. We perform consistent dimensional reduction of the heterotic theory on the warped $\mathbb R\times T^{1,1}$ internal space and obtain ${\cal N}=1$, $D=4$ supergravity, with one complex scalar multiplet and $SU(2)\times SU(2)$ Yang-Mills multiplets, where the gauge symmetry is originated from the isometry group of $T^{1,1}$.
We compactify the ten-dimensional spacetime in heterotic supergravity leaving four-dimensional Minkowski spacetime. We search for nonsupersymmetric, non-Ricci-flat solutions of the equations of motion with the quadratic curvature term. By assuming that the extradimensional spaces are products of 2-manifolds, three types of solutions are found. They are $S^2\times T^2 \times H^2/Γ$, $S^2\times H^2/Γ\times H^2/Γ$, and $S^2\times S^2 \times H^2/Γ$, where $H^2/Γ$ denotes a compact hyperbolic manifold. The metrics can be written explicitly, and they can be applied to phenomenology.
We classify all warped product de-Sitter backgrounds in heterotic supergravity, up to two loops. We find that warped $dS_n$ backgrounds, with $n\ge 3$, are $\mathbb{R}^{1,n}\times M_{9-n}$, where $M_{9-n}$ is a $(9-n)$-dimensional Riemannian manifold. Moreover, we establish that warped $dS_2$ backgrounds are $AdS_3\times M_7$, where $M_7$ is a 7-dimensional Riemannian manifold.
Poly-vector deformations of heterotic supergravity solutions
Institute for Information Transmission Problems（信息传输问题研究所）；Moscow Institute of Physics and Technology（莫斯科物理技术学院）；Lomonosov Moscow State University（莫斯科罗蒙诺索夫国立大学）
We show that a choice of Pauli-Villars regulators allows the cancellation of all conformal and chiral anomalies in an effective field theory from Z_3 compactification of the heterotic string with two Wilson lines and an anomalous U(1).
We consider heterotic strings on a warped Eguchi-Hanson space with five-brane and line bundle gauge fluxes. The heterotic string admits an exact CFT description in terms of an asymmetrically gauged SU(2)xSL(2,R) WZW model, in a specific double scaling limit in which the blow-up radius and the string scale are sent to zero simultaneously. This allows us to compute the perturbative 6D spectra for these models in two independent fashions: i) Within the supergravity approximation we employ a representation dependent index; ii) In the double scaling limit we determine all marginal vertex operators …
Carrollian limit of NS-NS and Heterotic Supergravity
Universidad San Sebastián, Facultad de Ingeniería（塞巴斯蒂安大学工程学院）；University of Wroclaw, Faculty of Physics and Astronomy（弗罗茨瓦夫大学物理与天文学学院）；Universidad Nacional Autónoma de México, Departamento de Física de Altas Energías, Instituto de Ciencias Nucleares（墨西哥国立自治大学高能物理系核科学研究所）
We comment on the ubiquity of the so-called warped anti-de Sitter spacetimes in three-dimensional (2,0) supergravity theory. By using isometry-invariant tensors and simple counting, we prove their existence for arbitrary $(2,0)$ supergravity models suitably defined close to a minimal model. We also analyze their offshell supersymmetry and the supersymmetry of two geometric orbifolds.
We classify the geometries of the most general warped, flux AdS backgrounds of heterotic supergravity up to two loop order in sigma model perturbation theory. We show under some mild assumptions that there are no $AdS_n$ backgrounds with $n\not=3$. Moreover the warp factor of AdS$_3$ backgrounds is constant, the geometry is a product $AdS_3\times M^7$ and such solutions preserve, 2, 4, 6 and 8 supersymmetries. The geometry of $M^7$ has been specified in all cases. For 2 supersymmetries, it has been found that $M^7$ admits a suitably restricted $G_2$ structure. For 4 supersymmetries, $M^7$ has …
We consider 1+3-dimensional domain wall solutions of heterotic supergravity on a six-dimensional warped nearly Kähler manifold $X_6$ in the presence of gravitational and gauge instantons of tanh-kink type as constructed in [arXiv:1109.3552]. We include first order $α'$ corrections to the heterotic supergravity action, which imply a non-trivial Yang-Mills sector and Bianchi identity. We present a variety of solutions, depending on the choice of instantons, for the special case in which the SU(3) structure on $X_6$ satisfies $W_1^-=0$. The solutions preserve two real supercharges, which correspo…
On the Stability of Warped Anti-de Sitter Spaces in Supergravity
Politecnico di Torino（都灵理工大学）；INFN, Sezione di Torino（意大利国家核物理研究所都灵分部）；CEICO, Institute of Physics of the Czech Academy of Sciences（捷克科学院物理研究所）；Universidade de Santiago de Compostela（圣地亚哥德孔波斯特拉大学）；Texas A&M University（德克萨斯农工大学）；ENS de Lyon（里昂高等师范学校）
I construct solutions to the heterotic supergravity BPS-equations on products of Minkowski space with a non-symmetric coset. All of the bosonic fields are homogeneous and non-vanishing, the dilaton being a linear function on the non-compact part of spacetime.
We continue to study the BPS gauge five-brane solutions of codimension two in ten-dimensional heterotic supergravity. The geometry including the dilaton and the NS-NS $B$-field are sourced from the monopole chain in $\mathbb{R}^2 \times S^1$. We find that the geometry is asymptotically Ricci flat and the dilaton is no longer imaginary valued. These properties are contrasted with the smeared counterpart discussed in our previous paper. We perform the T-duality transformations of the solution and find that it never results in a non-geometric object.
We find a family of complete non-linear Kaluza-Kein reduction ansatze from type IIB supergravity to Romans' 6D $F(4)$ gauged supergravity in the bosonic sector. The reduction is over a sphere $S^2$ and a Riemann surface $Σ$, and depends on a pair of arbitrary locally holomorphic functions $\mathcal{A}_{\pm}$ on $Σ$. This family of reductions is inspired by the recent construction of 1/2 BPS supersymmetric warped $AdS_6$ solutions of IIB supergravity that depend on these same functions $\mathcal{A}_{\pm}$.
This paper constructs the reduction of heterotic $M$-theory in eleven dimensions to a supergravity model on a manifold with boundary in five dimensions using a Calabi-Yau three-fold. New results are presented for the boundary terms in the action and for the boundary conditions on the bulk fields. Some general features of dualisation on a manifold with boundary are used to explain the origin of some topological terms in the action. The effect of gaugino condensation on the fermion boundary conditions leads to a `twist' in the chirality of the gravitino which can provide an uplifting mechanism i…
We obtain a family of heterotic supergravity backgrounds describing non-Kahler warped conifolds with three-form flux and an Abelian gauge bundle, preserving N=1 supersymmetry in four dimensions. At large distance from the singularity the usual Ricci-flat conifold is recovered. By performing a Z_2 orbifold of the T^{1,1} base, the conifold singularity can be blown-up to a four-cycle, leading to a completely smooth geometry. Remarkably, the throat regions of the solutions, which can be isolated from the asymptotic Ricci-flat geometry using a double-scaling limit, possess a worldsheet CFT descrip…
We use Pauli-Villars regularization to evaluate the conformal and chiral anomalies in the effective field theories from Z3 and Z7 compactifications of the heterotic string without Wilson lines. We show that parameters for Pauli-Villars chiral multiplets can be chosen in such a way that the anomaly is universal in the sense that its coefficient depends only on a single holomorphic function of the three diagonal moduli. It is therefore possible to cancel the anomaly by a generalization of the four-dimensional Green-Schwarz mechanism. In particular we are able to reproduce the results of a string…
We analyze the AdS_3 x M_7 type supersymmetric solutions, including non-trivial fluxes, of the Killing spinor equations in the heterotic supergravity. We classify these solutions by their G-structures and intrinsic torsions, for the cases that the number of seven-dimensional Killing spinors N are equal to 1,2,3 and 4. We find that the solutions cannot have non-trivial warp factor and the seven dimensional manifold M_7 is charactrized by G_2(SU(3))-structures for N=1 (2) case and SU(2)-structure for N=3 and 4 cases. They are further classified by their non-trivial intrinsic torsions. It is show…
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…
We study T-duality chains of five-branes in heterotic supergravity where the first order $α'$-corrections are present. By performing the $α'$-corrected T-duality transformations of the heterotic NS5-brane solutions, we obtain the KK5-brane and the exotic $5^2_2$-brane solutions associated with the symmetric, the neutral and the gauge NS5-branes. We find that the Yang-Mills gauge field in these solutions satisfies the self-duality condition in the three- and two-dimensional transverse spaces to the brane world-volumes. The $O(2,2)$ monodromy structures of the $5^2_2$-brane solutions are investi…
We construct a family of chiral anomaly-free supergravity theories in D=6 starting from D=7 supergravity with a gauged noncompact R-symmetry, employing a Horava-Witten bulk-plus-boundary construction. The gauged noncompact R-symmetry yields a positive (de Sitter sign) D=6 scalar field potential. Classical anomaly inflow which is needed to cancel boundary-field loop anomalies requires careful consideration of the gravitational, gauge, mixed and local supersymmetry anomalies. Coupling of boundary hypermultiplets requires care with the Sp(1) gauge connection required to obtain quaternionic Kahler…
On The Consistent Supersymmetric Reduction Of Heterotic Supergravity With Geometrically Arising Yang-Mills Symmetries
George P. & Cynthia Woods Mitchell Institute for Fundamental Physics and Astronomy, Texas A&M University（乔治·P和辛西娅·伍兹基础物理与天文学研究所，德克萨斯农工大学）；DAMTP, Centre for Mathematical Sciences, Cambridge University（剑桥大学数学科学中心DAMTP）
This work revisits the notions of connection and curvature in generalized geometry, with emphasis on torsion-free generalized connections on a transitive Courant algebroid, compatible with a generalized metric. Non-exact Courant algebroids have been considered recently by R. Rubio in the context of $B_n$-generalised geometry and arise naturally from the theory of generalized reduction of Burzstyn, Cavalcanti and Gualtieri. As an application, we provide a mathematical derivation of the equations of motion of heterotic supergravity, inspired by the work of Coimbra, Strickland-Constable and Waldr…
We present various (0,2) heterotic supercurrent supermultiplets in (1+1) dimensional quantum field theories. From the minimal supercurrent supermultiplets, we deduce conditions on symmetry enhancement such as Lorentz invariance, (chiral) dilatation invariance, R-invariance, (chiral) conformal invariance and their various combinations. Our construction covers many interesting and/or exotic possibilities such as Lifshitz supersymmetry and warped superconformal algebra. We also discuss the corresponding supergravity by gauging the supercurrent supermultiplet. In particular, we propose a novel cla…
We study a supersymmetry-preserving solution-generating method in heterotic supergravity. In particular, we use this method to construct one-parameter non-Kahler deformations of Calabi-Yau manifolds with a U(1) isometry, in which the complex structure remains invariant. We explain how to obtain corresponding solutions to heterotic string theory, up to first order in α', by a modified form of the standard embedding. In the course of the paper we also show that Abelian heterotic supergravity embeds into type II supergravity, and note that the solution-generating method in this context is related…
Heterotic supergravity with (1+3)--dimensional domain wall configurations and (warped) internal, six dimensional, almost-Kähler manifolds $\ ^6\mathbf{X}$ are studied. Considering ten dimensional spacetimes with nonholonomic distributions and conventional double fibrations, 2+2+...=2+2+3+3, and associated $SU(3)$ structures on internal space, we generalize for real, internal, almost symplectic gravitational structures the constructions with gravitational and gauge instantons of tanh-kink type. They include the first $α^{\prime}$ corrections to the heterotic supergravity action, parameterized i…
We determine the most general form of off-shell N=(1,1) supergravity field configurations in three dimensions by requiring that at least one off-shell Killing spinor exists. We then impose the field equations of the topologically massive off-shell supergravity and find a class of solutions whose properties crucially depend on the norm of the auxiliary vector field. These are spacelike-squashed and timelike-stretched AdS_3 for the spacelike and timelike norms, respectively. At the transition point where the norm vanishes, the solution is null warped AdS_3. This occurs when the coefficient of th…
We discuss Kaluza-Klein theory for type $II\ b $ supergravity on the warped deformed conifold using a large radial distance limit of Klebanov-Strassler solution where the radial coordinate separates from angle coordinates for a background asymptotic to $ AdS _5 \times T^{1,1}$ spacetime. The decomposition of field fluctuations on harmonics of the base manifold $T^{1,1}$ and plane waves of $M_4= ð(AdS _5 )$ is examined for the metric tensor components along $M_4= ð(AdS _5 )$, the axio-dilaton and the 4-form potential components along $T^{1,1}$. Semi-classical methods are used to compute the mas…
We consider the generalization of the heterotic action considered by Cherkis and Schwarz where the chiral bosons are introduced in a manifestly covariant way using an auxiliary field. In particular, we construct the kappa-symmetric heterotic action in ten-dimensional supergravity background coupled to super Yang-Mills theory and prove its kappa-symmetry. The usual Bianchi identity of Type I supergravity with super Yang-Mills $dH_3= -\tr F\wedge F$ is crucially used. For technical reason, the Yang-Mills field is restricted to be abelian.
The dimensional reduction of heterotic supergravity with gauge fields truncated to the Cartan subalgebra exhibits a continuous O(d,d+16;R) global symmetry, related to the O(d,d+16;Z) T-duality of heterotic strings on a d-torus. The O(d,d+16;R) symmetry is not present, however, if the supergravity reduction is done including the full set of E_8 x E_8 or SO(32) gauge fields. We analyze which duality symmetries are realized to all orders in $α'$ in the proper effective field theories for the massless string states. We find a universal O(d,d;R) symmetry, also predicted by double field theory. We c…
We dimensionally reduce the ten dimensional heterotic action on spacetimes of the form ${\cal M}_{(2,1)}\times Y$, where ${\cal M}_{(2,1)}$ is three dimensional maximally symmetric Anti de Sitter or Minkowski space, and $Y$ is a compact seven dimensional manifold with $G_2$ structure. In doing so, we derive the real superpotential functional of the corresponding three dimensional ${\cal N}=1$ theory. We confirm that extrema of this functional precisely correspond to supersymmetric heterotic compactifications on manifolds of $G_2$ structure. We make some comments on the role of the superpotenti…
