Supersymmetric double field theory: A stringy reformulation of supergravity

Abstract

We construct a supersymmetric extension of double field theory that realizes the ten-dimensional Majorana-Weyl local supersymmetry. In terms of a stringy differential geometry we proposed earlier, our action consists of five simple terms -two bosonic plus three fermionic -and manifests not only diffeomorphism and one-form gauge symmetry of B-field, but also O(10, 10) T-duality as well as a direct product of two local Lorentz symmetries, SO(1, 9) × SO(9, 1). A gauge fixing that identifies the double local Lorentz groups reduces our action to the minimal supergravity in ten dimensions.PACS numbers: 04.60. Cf, 04.65.+e Without resorting to vector notation, Maxwell's original equations consisted of twenty formulas. It was the rotational or Lorentz symmetry that reorganized them into four or two compact equations. Recent developments in string theory indicate that supergravity theories -at least those which have stringy origin -may undergo a similar reformulation, and be greatly simplified with the renewed understanding of their stringy structure or T-duality.T-duality is a genuine stringy effect such that string theory effective actions or ten-dimensional supergravities should feature O(10, 10) structure [1][2][3][4]. The O(10, 10) T-duality can be manifestly realized if we formally double the spacetime dimension, from ten to twenty with coordinates x µ → y A = (x µ , x ν ) [5][6][7][8], and reformulate the ten-dimensional effective action in terms of twenty dimensional language i.e. tensors equipped with O(10, 10) metric,This kind of reformulation was coined Double Field Theory (DFT) [9][10][11][12], and has attracted much attention in recent years [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31]. In DFT, as a field theory counterpart to the level matching condition of closed string theories, the O(10, 10) d'Alembertian operator must be trivial, acting on arbitrary fields as well as their products,Hence locally, up to O(10, 10) rotation, all the fields are independent of the dual coordinates, ∂ ∂xµ ≡ 0, and the theory is not truly doubled [11].In a sense, the O(10, 10) structure in DFT is a "metasymmetry" rather than a Noether symmetry, since only after dimensional reductions can it generate a Noether symmetry. Another feature of DFT is that, the diffeomorphism and the one-form gauge symmetry of B-field are naturally unified into what we may call "double-gauge symmetry," as they are generated by the generalized Lie derivative [8,12,[32][33][34],where ω T is the weight of T A1···An . Since this differs from the ordinary Lie derivative, the underlying differential geometry of DFT is not Riemannian [7, 8, 14-16, 18, 32-37] (see [38,39] for extensions to M-theory). Namely, while doubling the spacetime dimension is sufficient to manifest the O(10, 10) structure, the double-gauge symmetry (3) calls for novel mathematical treatment.In this paper, we construct a supersymmetric extension of double field theory that manifests simultaneously O(10, 10) T-duality and various gauge symmetries lis...

Heterotic α’-corrections in Double Field Theory

“…Supersymmetric DFT was constructed in [1][2][3][10][11][12] and more recently in gauged DFT in [63]. As explained in [23], the symmetry between the gauge and gravitational connections extends to the fermionic sector as well (more specifically the symmetry interchanges the gauginos with the curvature of the gravitinos), and this can be useful in the construction of the supersymmetric extension of our work.…”

“…A paradigmatic case is Double Field Theory (DFT), where T-duality is incorporated as a manifest symmetry of the universal supergravity sector [1][2][3][4][5]. The framework allows to incorporate heterotic vector fields [1][2][3]6], the Ramond-Ramond fields of type II theories [7][8][9][10] and the fermions that complete the supersymmetry multiplets [1][2][3][10][11][12]. This program led to the full covariantization of supergravities to lowest order in perturbation theory with respect to the T-duality symmetry of string theory.…”

Doubled α ′-geometry

“…The N = 1 supersymmetric form is contained in the superspace results of [11,12] and was worked out independently in explicit component form in [34]. (See also [35] for supersymmetric double field theory without vector multiplets.) The RamondRamond sector of type-II superstrings is given in [31,32], and its supersymmetric extension in [33].…”

U-duality covariant gravity

“…massive type II theories [11][12][13][14], and their supersymmetric extensions [1,[15][16][17][18], and also leads to a compelling generalization of Riemannian geometry [1,[19][20][21][22][23][24], which in turn is closely related to (and an extension of) results in the 'generalized geometry' of Hitchin and Gualtieri [25][26][27] (see [28][29][30][31][32][33][34] for other applications and [35][36][37][38] for reviews).…”