Physics Letters B 751 (2015) 408–412
Contents lists available at ScienceDirect
Physics Letters B
www.elsevier.com/locate/physletb
Superstring in doubled superspace
Igor Bandos
a,b,∗
a
Department of Theoretical Physics, University of the Basque Country UPV/EHU, P.O. Box 644, 48080 Bilbao, Spain
b
IKERBASQUE, Basque Foundation for Science, 48011, Bilbao, Spain
a r t i c l e i n f o a b s t r a c t
Article history:
Received
7 October 2015
Accepted
27 October 2015
Available
online 2 November 2015
Editor:
N. Lambert
The covariant and kappa-symmetric action for superstring in direct product of two flat D = 10 N = 1
superspaces
is presented. It is given by the sum of supersymmetric generalization of two copies of chiral
boson actions constructed with the use of the Pasti–Sorokin–Tonin (PST) technique. The chirality of 8
‘left’ bosons and 8 ‘left’ fermions and the anti-chirality of their ‘right’ counterparts are obtained as gauge
fixed version of the equations of motion, so that the physical degrees of freedom are essentially those
of the II Green–Schwarz superstring. Our action is manifestly T-duality invariant as the fields describing
oscillating and winding modes enter it on equal footing.
© 2015 The Author. Published by Elsevier B.V. This is an open access article under the CC BY license
(http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP
3
.
1. Introduction
The fact that, to make manifest T-duality, the characteristic
symmetry of String Theory [1], one needs to double the coordi-
nates
of the spacetime had been appreciated decades ago and the
corresponding sigma model actions were considered in [2] and [3].
The background fields coupled to the fundamental string should
also allow for formulation in doubled spacetime (or should be dou-
bled
themselves [4]); such a description is now known as ‘double
field theory’ [5].
The
pseudoaction of sigma model on doubled twisted tori was
proposed in [6] (where ‘pseudo’ refers to the fact that a chiral-
ity/self-duality
condition has to be imposed by hand when working
with the action) while Tseytlin’s action for this case was studied
in [7]. The covariant version of Tseytlin’s action was constructed
in [8] with the use of Pasti–Sorokin–Tonin (PST) technique [9] (see
also [10]). The relationship of the covariant pseudo-action [6] and
non-covariant action [3] was the subject of [11], where the PST
action of [8] was also reproduced. However, neither a supersym-
metric
generalization of the PST-type covariant action from [8] nor
a supersymmetric generalization of the non-covariant Tseytlin’s ac-
tion
[3] has been known before.
A
superstring model in an enlarged doubled superspace was
proposed recently [12] (see also [13]). This model is not just
the supersymmetric and covariant generalization of Tseytlin’s
action as a number of additional types of coordinates are in-
*
Correspondence to: Department of Theoretical Physics, University of the Basque
Country UPV/EHU, P.O. Box 644, 48080 Bilbao, Spain.
E-mail
address: igor.bandos@ehu.eus.
troduced besides the doubling of bosonic vector coordinates
of superspace. The approach of [12] is based on an embed-
ding
of (two) super-Poincaré algebra(s) into a superalgebra with
nondegenerate metric; extra coordinates are then partially re-
moved
by imposing dimensional reduction and section condi-
tions.
In
this letter we develop a more economic description of the
T-duality invariant type II superstring. We present the PST action
for supersymmetric string in double D = 10, N = 1superspace
and describe its gauge symmetries, including the local fermionic
κ-symmetry. Our action is a supersymmetric generalization of the
bosonic string PST action from [11] and the nontrivial part of our
study was the search for κ -symmetry. The preservation of the
κ-symmetry may be considered as a guide to search for super-
space
constraints describing supergravity in doubled superspace
(see [14,15] for the description of supergravity in double space
1
and [22,23] for its description in a very extended doubled super-
space).
We
denote the coordinates of two copies, left,
(10|16)
L
, and
right,
(10|16)
R
, of the D =10, N = 1superspace by
Z
M
L
= (X
a
L
,θ
α1
) and Z
˜
M
R
= (X
˜
a
R
,θ
˜
α2
) (1)
with a = 0, 1, ..., 9 and α = 1, ..., 16. Their push-forwards to
the worldsheet W
2
(with local coordinates {ξ
m
}), which we will
denote by the same symbols, will describe the left-moving and
1
M-theoretic counterparts in enlarged spaces with manifest U-duality symmetry
were studied in [17] and [21,18,19]; their purely bosonic counterparts had been
proposed in [16] and [20].
http://dx.doi.org/10.1016/j.physletb.2015.10.081
0370-2693/
© 2015 The Author. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by
SCOAP
3
.
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