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Anomalous U(1)'s in Type I and Type IIB D=4, N=1 string vacua

L. E. Ibanez, R. Rabadan, A. M. Uranga

TL;DR

This paper shows that 4D, N=1 string vacua of Type I and Type IIB with D-branes generically contain multiple anomalous U(1)s. Anomalies are canceled through a generalized Green-Schwarz mechanism using twisted RR scalars, with untwisted fields decoupled from the cancellation and FI terms controlled by NS-NS partners of twisted RR fields. The mechanism allows anomalous U(1) gauge bosons to remain arbitrarily light and yields explicit factorization constraints that tie into tadpole conditions and brane configurations, including D3-branes at orbifold/orientifold singularities and brane-box models. The work also constructs new large families of N=1 chiral theories and discusses the phenomenological implications of these twisted RR-based anomaly cancellations, highlighting key differences from heterotic vacua.

Abstract

We study the cancellation of U(1) anomalies in Type I and Type IIB D=4, N=1 string vacua. We first consider the case of compact toroidal $Z_N$ Type IIB orientifolds and then proceed to the non-compact case of Type IIB D3 branes at orbifold and orientifold singularities. Unlike the case of the heterotic string we find that for each given vacuum one has generically more than one U(1) with non-vanishing triangle anomalies. There is a generalized Green-Schwarz mechanism by which these anomalies are cancelled. This involves only the Ramond-Ramond scalars coming from the twisted closed string spectrum but not those coming from the untwisted sector. Associated to the anomalous U(1)'s there are field-dependent Fayet-Illiopoulos terms whose mass scale is fixed by undetermined vev's of the NS-NS partners of the relevant twisted RR fields. Thus, unlike what happens in heterotic vacua, the masses of the anomalous U(1)'s gauge bosons may be arbitrarily light. In the case of D3 branes at singularities, appropriate factorization of the U(1)'s constrains the Chan-Paton matrices beyond the restrictions from cancellation of non-abelian anomalies. These conditions can be translated to constraints on the T-dual Type IIB brane box configurations. We also construct a new large family of N=1 chiral gauge field theories from D3 branes at orientifold singularities, and check its non-abelian and U(1) anomalies cancel.

Anomalous U(1)'s in Type I and Type IIB D=4, N=1 string vacua

TL;DR

This paper shows that 4D, N=1 string vacua of Type I and Type IIB with D-branes generically contain multiple anomalous U(1)s. Anomalies are canceled through a generalized Green-Schwarz mechanism using twisted RR scalars, with untwisted fields decoupled from the cancellation and FI terms controlled by NS-NS partners of twisted RR fields. The mechanism allows anomalous U(1) gauge bosons to remain arbitrarily light and yields explicit factorization constraints that tie into tadpole conditions and brane configurations, including D3-branes at orbifold/orientifold singularities and brane-box models. The work also constructs new large families of N=1 chiral theories and discusses the phenomenological implications of these twisted RR-based anomaly cancellations, highlighting key differences from heterotic vacua.

Abstract

We study the cancellation of U(1) anomalies in Type I and Type IIB D=4, N=1 string vacua. We first consider the case of compact toroidal Type IIB orientifolds and then proceed to the non-compact case of Type IIB D3 branes at orbifold and orientifold singularities. Unlike the case of the heterotic string we find that for each given vacuum one has generically more than one U(1) with non-vanishing triangle anomalies. There is a generalized Green-Schwarz mechanism by which these anomalies are cancelled. This involves only the Ramond-Ramond scalars coming from the twisted closed string spectrum but not those coming from the untwisted sector. Associated to the anomalous U(1)'s there are field-dependent Fayet-Illiopoulos terms whose mass scale is fixed by undetermined vev's of the NS-NS partners of the relevant twisted RR fields. Thus, unlike what happens in heterotic vacua, the masses of the anomalous U(1)'s gauge bosons may be arbitrarily light. In the case of D3 branes at singularities, appropriate factorization of the U(1)'s constrains the Chan-Paton matrices beyond the restrictions from cancellation of non-abelian anomalies. These conditions can be translated to constraints on the T-dual Type IIB brane box configurations. We also construct a new large family of N=1 chiral gauge field theories from D3 branes at orientifold singularities, and check its non-abelian and U(1) anomalies cancel.

Paper Structure

This paper contains 10 sections, 64 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Anomalous $U(1)$'s in Type I and Type IIB $D=4$, $N=1$ vacua
  3. Anomalous $U(1)$s in compact Type IIB $D=4$, $N=1$ orientifolds
  4. Examples
  5. Brane-box models and D3-branes at $Z_N$ orbifold and orientifold singularities
  6. D3 branes at orbifold singularities
  7. D3 branes at orientifold singularities
  8. Fayet-Illiopoulos terms
  9. Final comments
  10. Appendix

Figures (2)

  • Figure 1: The three graphs contributing to the mixed $U(1)_i \times G_j^2$ mixed anomaly. The first two, the annulus (a) and Moebius strip (b), give the usual triangle anomaly of field theory. The last diagram (c), the non-planar annulus, cancels the contribution from the first two.
  • Figure 2: The annulus diagram of Figure 1c in the closed string channel. Twisted RR fields propagating along the cylinder provide the contribution that cancels the anomaly.