超弦理论：双倍超空间中的协变与κ对称性

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"Igor Bandos在Physics Letters B 751 (2015) 408–412发表的文章《超弦在超双倍空间中的研究》探讨了在两个平坦的D = 10 N = 1超空间直接积中的超弦的协变和κ对称作用。该研究利用Pasti-Sorokin-Tonin (PST) 技术，将两个手性玻色子作用的超对称泛化之和构建为超弦的行动原理。" 这篇论文中，作者提出了一个重要的概念——超双倍空间中的超弦理论。超双倍空间是指将两个具有相同维度和超对称性的平坦超空间直接相乘的结果，这样的构造允许研究者在一个统一的框架下处理时空和其双线性变换（如T-对称性）的关系。D = 10 N = 1超空间指的是具有10维时空和一个N = 1超对称性的理论，这里的N表示超对称的生成元数量。 κ对称性是超弦理论中的关键特性，它确保了理论的物理状态是无 ghosts（即负能量的不稳定量子态）的，并且能有效地减少不必要的自由度。κ对称性作用的协变性意味着该理论在κ变换下保持不变，这是一种特定的规范变换，可以用来消除超弦的多余度。论文中，通过Pasti-Sorokin-Tonin (PST) 技术，作者构造了超弦的行动。PST技术是一种用于构造无扭力的超弦理论的工具，它可以处理超弦的运动方程并保持超对称性。在这种情况下，PST方法被用来将两个手性玻色子的作用泛化，从而得到超弦的总作用。在运动方程的规范固定形式下，文章得到了8个左手玻色子和8个左手费米子的 chirality（手征性），以及它们的右手对应物的反手征性。这意味着理论中包含了正确的物理自由度，与II型格林-施瓦茨超弦理论（IIA或IIB型）的物理学位相匹配。这里的“左”和“右”指的是粒子的 chirality，手征性是粒子在空间中的自旋方向与行进方向的关联。 T-对称性是弦理论中的另一个重要性质，它涉及到理论在不同背景下的等价性，特别是当弦振动模式在紧致化维度上发生变化时。文中指出，提出的超弦行动是显式T-对称的，这意味着理论的场描述能够直接反映T-对称性，这对于理解和构建T-对称变换下的不变理论至关重要。这篇论文为超弦理论在超双倍空间中的理解和应用提供了一个新的视角，同时强调了κ对称性和T-对称性的关键角色，以及PST技术在构造有效行动中的实用价值。这些研究成果对于深入理解弦理论的数学结构和物理内涵，以及在高维宇宙模型和量子引力等领域有着深远的影响。

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,∗

Department of Theoretical Physics, University of the Basque Country UPV/EHU, P.O. Box 644, 48080 Bilbao, Spain

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.

(http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP

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.

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.

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

and [22,23] for its description in a very extended doubled super-

space).

denote the coordinates of two copies, left, 

(10|16)

, and

right, 

(10|16)

, of the D =10, N = 1superspace by

= (X

,θ

α1

) and Z

= (X

,θ

α2

) (1)

with a = 0, 1, ..., 9 and α = 1, ..., 16. Their push-forwards to

the worldsheet W

(with local coordinates {ξ

}), which we will

denote by the same symbols, will describe the left-moving and

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/

SCOAP

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