Strong/weak coupling duality relations for non-supersymmetric string theories

Abstract

Both the supersymmetric SO(32) and E 8 × E 8 heterotic strings in ten dimensions have known strong-coupling duals. However, it has not been known whether there also exist strong-coupling duals for the non-supersymmetric heterotic strings in ten dimensions. In this paper, we construct explicit open-string duals for the circle-compactifications of several of these non-supersymmetric theories, among them the tachyon-free SO(16) × SO(16) string. Our method involves the construction of heterotic and open-string interpolating models that continuously connect non-supersymmetric strings to supersymmetric strings. We find that our non-supersymmetric dual theories have exactly the same massless spectra as their heterotic counterparts within a certain range of our interpolations. We also develop a novel method for analyzing the solitons of non-supersymmetric open-string theories, and find that the solitons of our dual theories also agree with their heterotic counterparts. These are therefore the first known examples of strong/weak coupling duality relations between nonsupersymmetric, tachyon-free string theories. Finally, the existence of these strong-coupling duals allows us to examine the non-perturbative stability of these strings, and we propose a phase diagram for the behavior of these strings as a function of coupling and radius* Throughout this paper, we shall use the phrase "Type I" to indicate the general class of openstring theories, regardless of whether they have spacetime supersymmetry. Similarly, we shall use the phrase "Type II" to signify closed strings with left-and right-moving worldsheet supersymmetry, regardless of whether they have spacetime supersymmetry. These terms will therefore be used in the same way as the general term "heterotic". * Note, in particular, that we are only algebraically rewriting the loop amplitude, not constructing to the tree amplitude, and consequently we may simply define t ′ = 1/t as a convenient variable and do not require the tree variable ℓ = 1/8t.

Non-perturbative transitions among intersecting-brane vacua

“…There is a large literature on non-supersymmetric string vacua built over the years, in the heterotic strings [5][6][7][8][9][10][11], type 0 orientifolds [12,13], type II orientifolds with supersymmetry broken by compactification [14][15][16][17], by magnetic fields [3,[18][19][20][21][22][23][24][25], at the string scale [26][27][28][29][30] or by a combination of these effects [31,32]. Although most of the non-supersymmetric vacua are manifestly unstable at the classical level due to the tachyonic states appearing in some regions of the moduli space some, most notably the models with "Brane Supersymmetry Breaking" [26][27][28][29][30] have no manifest classical instabilities.…”

Magnetic backgrounds and tachyonic instabilities in closed string theory

“…This relation between type II and type 0 string theories may be expressed by saying that type 0 string is (a limit of) type II string compactified on a circle with antiperiodic boundary conditions for space-time fermions [9]. More precisely, the two theories are the limits of the same interpolating "9-dimensional" string theory [11] -Σ R orbifold of type II theory. Σ R stands for (S 1 ) R /[(−1) Fs × S], where S is half-shift along the circle (X 9 → X 9 + πR).…”

“…4 Type IIA on Σ R→∞ is type IIA theory in flat d = 10 and type IIA on Σ R→0 is type 0A theory on (S 1 ) R→0 (or T-dual type 0B theory on (S 1 ) R→∞ ). Thus the Σ R orbifold type IIA theory (which has massive fermions in its spectrum) continuously interpolates between supersymmetric type IIA and non-supersymmetric type 0B ten-dimensional theories [11].…”

“…In the second M-theory description of type 0A theory -as M-theory in the background (12) at the critical magnetic fieldbR 9 = 1 the type 0A tachyon corresponds to an unstable mode in the momentum part of the spectrum which may be thus seen directly in d = 10 or d = 11 supergravity spectra in the corresponding curved backgrounds (7) and (12). 11 This setting thus allows one to interpret the type 0A tachyon as a particular fluctuation mode of d = 11 supergravity expanded near (12). The solution of the relevant Laplace operatore has the following structure [8] M 2 = p 2 9 + p 2 11 +b 2 J 2 + 2b p 2 9 + p 2 11 (l L + l R + 1 − S R + S L ) ,…”

“…Antiperiodic fermions appear in the context of superstrings at finite temperature [9] and in closely related type 0 string theory viewed as (−1) Fs orbifold of type II superstring theory [10,11].…”