9911064 O ( d , d ) invariance at two and three loops

نویسنده

  • S. Parsons
چکیده

We show that in a two-dimensional σ-model whose fields only depend on one target space coordinate , the O(d, d) invariance of the conformal invariance conditions observed at one loop is preserved at two loops (in the general case with torsion) and at three loops (in the case without torsion). Duality invariance has proved to be an immensely fruitful concept in string theory. A particular aspect of duality which has been valuable in string cosmology (for a recent comprehensive review of this subject, with an extensive list of references, see Ref. [1]) is the concept of O(d, d) invariance. This is displayed in the case where the fields depend only on time in an arbitrary number of dimensions (time and d spatial dimensions). It was discovered some time ago[2] that the lowest order string effective action (in the simplest case with only the metric, dilaton and antisymmetric tensor field) then exhibits continuous, global O(d, d) invariance. (This is also reminiscent of the O(d, d) invariance previously observed in the context of string compactifications[3].) The O(d, d) invariance of the string action was later found to persist in the presence of matter or gauge fields[4]. Now the conformal invariance conditions for the fields are related to the field equations of the string action, and so, at least at lowest order, the O(d, d) invariance can be used to transform between different conformal backgrounds. Duality invariance in general can be understood as a consequence of an isometry in an underlying theory[5]; and the O(d, d) invariance can be viewed as the result of gauging d abelian isometries[6]. In Refs. [2] and [7] it was argued that the O(d, d) invariance should be maintained to all orders. In Ref. [8] the two-loop string action was considered in the context of fields depending only on time, and it was shown that after a suitable field redefinition it could be written in an explicitly O(d, d) invariant form. However, it was pointed out in Ref. [9] (in the context of T duality) that the invariance of the action does not manifestly guarantee that the conformal invariance conditions transform appropriately. Therefore it seems to us that it is necessary to check explicitly the transformation properties of the conformal invariance conditions in order to complete the proof that O(d, d) invariance is preserved. At one loop this has been done in Ref. [2]. The main purpose of …

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

O ( d , d ) invariance at two and three loops

We show that in a two-dimensional σ-model whose fields only depend on one target space coordinate , the O(d, d) invariance of the conformal invariance conditions observed at one loop is preserved at two loops (in the general case with torsion) and at three loops (in the case without torsion). Duality invariance has proved to be an immensely fruitful concept in string theory. A particular aspect...

متن کامل

Size influence on shape of handwritten characters loops.

In the practice of forensic handwriting experts, the size of the writing on a questioned document may be different from that of known samples. In this study, the hypothesis of shape invariance of handwritten closed loops across size increasing was tested. A Fourier methodology was applied to 2325 small letters (591 a loops, 547 d loops, 596 o loops and 591 q loops) and 692 enlarged letters (162...

متن کامل

The concept of logic entropy on D-posets

In this paper, a new invariant called {it logic entropy} for dynamical systems on a D-poset is introduced. Also, the {it conditional logical entropy} is defined and then some of its properties are studied.  The invariance of the {it logic entropy} of a system  under isomorphism is proved. At the end,  the notion of an $ m $-generator of a dynamical system is introduced and a version of the Kolm...

متن کامل

Solving the tandem AGV network design problem using tabu search: Cases of maximum workload and workload balance with fixed and non-fixed number of loops

A tandem AGV configuration connects all cells of a manufacturing area by means of non-overlapping, sin-gle-vehicle closed loops. Each loop has at least one additional P/D station, provided as an interface between adjacent loops. This study describes the development of three tabu search algorithms for the design of tandem AGV systems. The first algorithm was developed based on the basic definiti...

متن کامل

Increasing Performance and Thermostability of D-Phenylglycine Aminotransferase in Miscible Organic Solvents

Background: D-Phenylglycine aminotransferase (D-PhgAT) is highly beneficial in pharmaceutical biotechnology. Like many other enzymes, D-PhgAT suffers from low stability under harsh processing conditions, poor solubility of substrate, products and occasional microbial contamination. Incorporation of miscible organic solvents into the enzyme’s reaction is considered as a solution...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 1999