More stringy effects in target space from Double Field Theory
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Springer
Received: May 28, 2020 Accepted: July 22, 2020 Published: August 24, 2020
Chen-Te Maa,b,c,d,1 and Franco Pezzellae a
Guangdong Provincial Key Laboratory of Nuclear Science, Institute of Quantum Matter, South China Normal University, Guangzhou 510006, Guangdong, China b School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou 510006, Guangdong, China c The Laboratory for Quantum Gravity and Strings, Department of Mathematics and Applied Mathematics, University of Cape Town, Private Bag, Rondebosch 7700, South Africa d Department of Physics and Center for Theoretical Sciences, National Taiwan University, Taipei 10617, Taiwan, R.O.C. e Istituto Nazionale di Fisica Nucleare — Sezione di Napoli, Complesso Universitario di Monte S. Angelo ed. 6, via Cintia, 80126 Napoli, Italy
E-mail: [email protected], [email protected]
1
Corresponding author.
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP08(2020)113
JHEP08(2020)113
More stringy effects in target space from Double Field Theory
Keywords: Bosonic Strings, Flux compactifications, String Duality, String Field Theory ArXiv ePrint: 1909.00411
JHEP08(2020)113
Abstract: In Double Field Theory, the mass-squared of doubled fields associated with bosonic closed string states is proportional to NL + NR − 2. Massless states are therefore not only the graviton, anti-symmetric, and dilaton fields with (NL = 1, NR = 1) such theory is focused on, but also the symmetric traceless tensor and the vector field relative to the states (NL = 2, NR = 0) and (NL = 0, NR = 2) which are massive in the lowerdimensional non-compactified space. While they are not even physical in the absence of compact dimensions, they provide a sample of states for which both momenta and winding numbers are non-vanishing, differently from the states (NL = 1, NR = 1). A quadratic action is therefore here built for the corresponding doubled fields. It results that its gauge invariance under the linearized double diffeomorphisms is based on a generalization of the usual weak constraint, giving rise to an extra mass term for the symmetric traceless tensor field, not otherwise detectable: this can be interpreted as a mere stringy effect in target space due to the simultaneous presence of momenta and windings. Furthermore, in the context of the generalized metric formulation, a non-linear extension of the gauge transformations is defined involving the constraint extended from the weak constraint that can be uniquely defined in triple products of fields. Finally, we show that the above mentioned stringy effect does not appear in the case of only one compact doubled space dimension.
Contents 1 Introduction
1
2 Quadratic theory
3
3 Gauge transformation
8 10
5 Outlook
11
1
Introduction
When compactified on a d-dimensional torus T d , string theory exhibits the peculiar symmetry O(d, d; Z) [1] for all the d compact directions [2]: the target-space duality (Tduality) [3, 4]. It is a distinctive symmetry of string
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