Double Field Theory

By Chris Hull, B. Zwiebach. 2009

779 citations recorded by the source corpus.

The zero modes of closed strings on a torus — the torus coordinates plus dual coordinates conjugate to winding number — parameterize a doubled torus. In closed string field theory, the string field depends on all zero-modes and so can be expanded to give an infinite set of fields on the doubled torus. We use string field theory to construct a theory of massless fields on the doubled torus. Key to the consistency is a constraint on fields and gauge parameters that arises from the L0−0 = 0 condition in closed string theory. The symmetry of this double field theory includes usual and `dual diffeomorphisms', together with a T-duality acting on fields that have explicit dependence on the torus coordinates and the dual coordinates. We find that, along with gravity, a Kalb-Ramond field and a dilaton must be added to support both usual and dual diffeomorphisms. We construct a fully consistent and gauge invariant action on the doubled torus to cubic order in the fields. We discuss the challenges involved in the construction of the full nonlinear theory. We emphasize that the doubled geometry is physical and the dual dimensions should not be viewed as an auxiliary structure or a gauge artifact.

Subfields: Artificial Intelligence, Condensed Matter Physics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/df0dcd384e07d00c597621f148f52745932eba57

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

1. O. Hohm
2. David S. Berman
3. S. Kwak
4. D. Thompson
5. M. Perry
6. D. Marqués
7. H. Godazgar
8. C. Hull

In Condensed Matter Physics

1. O. Hohm
2. David S. Berman
3. S. Kwak
4. D. Thompson
5. M. Perry
6. D. Marqués
7. H. Godazgar
8. C. Hull

In Nuclear and High Energy Physics

1. D. Marqués
2. O. Hohm
3. David S. Berman
4. C. Nuñez
5. D. Thompson
6. G. Aldazabal
7. D. Waldram
8. D. Lust

Citations in the corpus

• Gauged Supergravities. (2016, neutral): “This is effected by either extending (doubling) the tangent space of Mint (generalized geometry [89],[90],[61]) or extending the space-time manifold itself (Double Geometry [91]-[94] or Double Field Theory [95]-[100]).”
• Doubled α′-geometry (2013, positive): “In more recent developments [14] the construction of such a double field theory was based on closed string field theory [15, 16].”
• Supergravity as generalised geometry I: type II theories (2011, neutral): “As we mentioned in the introduction, both in Siegel’s formulation [14, 15] and in doubled field theory [16], if one requires the action to be gauge invariant, one imposes the condition that on each coordinate patch the fields are independent of half the doubled coordinates.”
• The effective action of double field theory (2011, positive): “For T-duality this was successfully achieved by Double Field Theory (DFT), originally formulated in [25]–[28] and extended in [29]–[39].”
• Extended geometry and gauged maximal supergravity (2013, background): “The program to rewrite the theory in a covariant language under O(d, d), the group that includes T-duality, goes under the name of Generalized Geometry [1, 2], or Double Field Theory (DFT) [3–6] (the latter based on previous constructions on”
• Duality invariant M-theory: gauged supergravities and Scherk-Schwarz reductions (2012, positive): “Describing the properties of these manifolds will be an interesting direction for future study – in [47] recent progress in this direction has been made in understanding how to “exponentiate” the local symmetries for the O(d, d) case relevant to DFT.”
• Double field theory: a pedagogical review (2013, neutral): “Double Field Theory (DFT) [1, 2] is a proposal to incorporate T-duality, a distinctive symmetry of string (or M-)theory, as a symmetry of a field theory.”
• On the Riemann tensor in double field theory (2011, neutral): “Specifically, here the space-time coordinates are doubled in order to realize the ‘T-duality group’ O(D,D) geometrically, while introducing an O(D,D) covariant constraint that locally removes the dependence on half of the coordinates [1–4].”
• L∞ algebras and field theory (2017, neutral): “A particularly interesting case is that of double field theory as envisioned in [25], where one would include the Kaluza-Klein and winding modes associated with the massless fields of string theory in toroidal backgrounds.”
• Frame-like geometry of double field theory (2010, positive): “Specifically, introducing the following change of basis for the gauge parameters (which is suggested by the gauge structure in string field theory [6]),”
• Generalized metric formulation of double field theory (2010, neutral): “Double field theory [2, 3, 4] is a field theoretic approach inspired by closed string field theory [5, 6] that focuses on the gravity, antisymmetric tensor, and dilaton fields.”
• Duality invariant actions and generalised geometry (2011, positive): “The extra dimensions are M-theoretic generalisations of the winding coordinates found in doubled field theory [40, 41, 42, 43].”
• Supergravity as generalised geometry II: Ed(d) × ℝ+ and M theory (2014, positive): “In the bosonic sector, a more recent approach is the work of Berman and Perry and collaborators [21], using the M-theory extension of double field theory [33, 34].”
• The spacetime of double field theory: Review, remarks, and outlook (2013, positive): “In fact, the gauge transformations to cubic order have been derived from closed string field theory [4], and there is a unique way to make them background independent as transformations of gij and bij [6].”
• Large gauge transformations in double field theory (2012, neutral): “This theory has been formulated in [1–4].”