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Register a new userSupersymmetric gauged Double Field Theory: Systematic derivation by virtue of textit{Twist}
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In a completely systematic and geometric way, we derive maximal and half-maximal supersymmetric gauged double field theories in lower than ten dimensions. To this end, we apply a simple twisting ansatz to the $D=10$ ungauged maximal and half-maximal supersymmetric double field theories constructed previously within the so-called semi-covariant formalism. The twisting ansatz may not satisfy the section condition. Nonetheless, all the features of the semi-covariant formalism, including its complete covariantizability, are still valid after the twist under alternative consistency conditions. The twist allows gaugings as supersymmetry preserving deformations of the $D=10$ untwisted theories after Scherk-Schwarz-type dimensional reductions. The maximal supersymmetric twist requires an extra condition to ensure both the Ramond-Ramond gauge symmetry and the $32$ supersymmetries unbroken.
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In four spacetime dimensions, all ${cal N} =1$ supergravity-matter systems can be formulated in the so-called $mathsf{U}(1)$ superspace proposed by Howe in 1981. This paper is devoted to the study of those geometric structures which characterise a background $mathsf{U}(1)$ superspace and are important in the context of supersymmetric field theory in curved space. We introduce (conformal) Killing tensor superfields $ell_{(alpha_1 dots alpha_m) ({dot alpha}_1 dots {dot alpha}_n)}$, with $m$ and $n$ non-negative integers, $m+n>0$, and elaborate on their significance in the following cases: (i) $m=n=1$; (ii) $m-1=n=0$; and (iii) $m=n>1$. The (conformal) Killing vector superfields $ell_{alpha dot alpha}$ generate the (conformal) isometries of curved superspace, which are symmetries of every (conformal) supersymmetric field theory. The (conformal) Killing spinor superfields $ell_{alpha }$ generate extended (conformal) supersymmetry transformations. The (conformal) Killing tensor superfields with $m=n>1$ prove to generate all higher symmetries of the (massless) massive Wess-Zumino operator.
To the full order in fermions, we construct D=10 type II supersymmetric double field theory. We spell the precise N=2 supersymmetry transformation rules as for 32 supercharges. The constructed action unifies type IIA and IIB supergravities in a manifestly covariant manner with respect to O(10,10) T-duality and a pair of local Lorentz groups, or Spin(1,9) times Spin(9,1), besides the usual general covariance of supergravities or the generalized diffeomorphism. While the theory is unique, the solutions are twofold. Type IIA and IIB supergravities are identified as two different types of solutions rather than two different theories.
Double Field Theory provides a geometric framework capable of describing string theory backgrounds that cannot be understood purely in terms of Riemannian geometry -- not only globally (`non-geometry), but even locally (`non-Riemannian). In this work, we show that the non-relativistic closed string theory of Gomis and Ooguri [1] arises precisely as such a non-Riemannian string background, and that the Gomis-Ooguri sigma model is equivalent to the Double Field Theory sigma model of [2] on this background. We further show that the target-space formulation of Double Field Theory on this non-Riemannian background correctly reproduces the appropriate sector of the Gomis-Ooguri string spectrum. To do this, we develop a general semi-covariant formalism describing perturbations in Double Field Theory. We derive compact expressions for the linearized equations of motion around a generic on-shell background, and construct the corresponding fluctuation Lagrangian in terms of novel completely covariant second order differential operators. We also present a new non-Riemannian solution featuring Schrodinger conformal symmetry.
We construct a double field theory coupled to the fields present in Vasilievs equations. Employing the semi-covariant differential geometry, we spell a functional in which each term is completely covariant with respect to $mathbf{O}(4,4)$ T-duality, doubled diffeomorphisms, $mathbf{Spin}(1,3)$ local Lorentz symmetry and, separately, $mathbf{HS}(4)$ higher spin gauge symmetry. We identify a minimal set of BPS-like conditions whose solutions automatically satisfy the full Euler-Lagrange equations. As such a solution, we derive a linear dilaton vacuum. With extra algebraic constraints further supplemented, the BPS-like conditions reduce to the bosonic Vasiliev equations.
Taking $mathbf{O}(D,D)$ covariant field variables as its truly fundamental constituents, Double Field Theory can accommodate not only conventional supergravity but also non-Riemannian gravities that may be classified by two non-negative integers, $(n,bar{n})$. Such non-Riemannian backgrounds render a propagating string chiral and anti-chiral over $n$ and $bar{n}$ dimensions respectively. Examples include, but are not limited to, Newton--Cartan, Carroll, or Gomis--Ooguri. Here we analyze the variational principle with care for a generic $(n,bar{n})$ non-Riemannian sector. We recognize a nontrivial subtlety for ${nbar{n} eq 0}$ that infinitesimal variations generically include those which change $(n,bar{n})$. This seems to suggest that the various non-Riemannian gravities should better be identified as different solution sectors of Double Field Theory rather than viewed as independent theories. Separate verification of our results as string worldsheet beta-functions may enlarge the scope of the string landscape far beyond Riemann.
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