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Exotic Branes and Symmetries of String Theory

Ashoke Sen

TL;DR

Exotic Branes and Symmetries of String Theory investigates whether duality transformations are genuine gauge symmetries by examining monodromies around codimension-two exotic branes in flat space versus AdS. It develops scaling arguments and energy analyses for macroscopic brane loops, showing that dualities act as spontaneously broken discrete gauge symmetries with observable consequences when loops are accessible. The work constructs and analyzes SL(2,Z) multiplets of strings and seven-branes, extends to other BPS branes, and demonstrates how to expose exotic branes through compactifications such as F-theory, M-theory on S^1/Z_2, and D8-brane setups, enabling empirical-like access to duality properties. It also discusses non-BPS branes and the limitations for flat codimension-one branes, clarifying the role of U-duality as a gauge symmetry in asymptotically flat string theory and distinguishing these results from AdS/CFT expectations.

Abstract

Are duality transformations symmetries of string theory? For AdS space-time the answer is no for generic asymptotic values of the moduli, since the duality symmetry is broken explicitly in the dual conformal field theory. In contrast, in string theory in flat space-time, monodromy around codimension two exotic branes show that duality transformations are spontaneously broken discrete gauge symmetries with observable consequences, provided macroscopic loops of these branes are not hidden behind an event horizon. We discuss how this can be achieved and how the situation in flat space-time differs from that in AdS space-time. We also discuss observability of codimension two non-BPS branes and codimension one BPS and non-BPS branes.

Exotic Branes and Symmetries of String Theory

TL;DR

Exotic Branes and Symmetries of String Theory investigates whether duality transformations are genuine gauge symmetries by examining monodromies around codimension-two exotic branes in flat space versus AdS. It develops scaling arguments and energy analyses for macroscopic brane loops, showing that dualities act as spontaneously broken discrete gauge symmetries with observable consequences when loops are accessible. The work constructs and analyzes SL(2,Z) multiplets of strings and seven-branes, extends to other BPS branes, and demonstrates how to expose exotic branes through compactifications such as F-theory, M-theory on S^1/Z_2, and D8-brane setups, enabling empirical-like access to duality properties. It also discusses non-BPS branes and the limitations for flat codimension-one branes, clarifying the role of U-duality as a gauge symmetry in asymptotically flat string theory and distinguishing these results from AdS/CFT expectations.

Abstract

Are duality transformations symmetries of string theory? For AdS space-time the answer is no for generic asymptotic values of the moduli, since the duality symmetry is broken explicitly in the dual conformal field theory. In contrast, in string theory in flat space-time, monodromy around codimension two exotic branes show that duality transformations are spontaneously broken discrete gauge symmetries with observable consequences, provided macroscopic loops of these branes are not hidden behind an event horizon. We discuss how this can be achieved and how the situation in flat space-time differs from that in AdS space-time. We also discuss observability of codimension two non-BPS branes and codimension one BPS and non-BPS branes.

Paper Structure

This paper contains 13 sections, 71 equations, 2 figures.

Table of Contents

  1. Introduction
  2. SL(2,$\mathbb{Z}$) multiplet of strings in four dimensions
  3. SL(2,$\mathbb{Z}$) multiplet of seven branes in type IIB theory
  4. Other codimension two BPS branes
  5. Scaling of macroscopic codimension two brane loops
  6. U-duality as gauge symmetries
  7. AdS vs flat space-time
  8. Non-BPS branes
  9. Exposing the exotic branes from compact dimensions
  10. (s,r) seven branes from F-theory compactification
  11. End of the world $E_8$ branes from M-theory compactification
  12. D8-branes in type I$'$ string theory
  13. Flat codimension one branes

Figures (2)

  • Figure 1: A string loop of coordinate radius $L_0$ in the $\theta=0$ plane.
  • Figure 2: This figure illustrates the maximum period during which an apparatus coming from side $A$ of the brane to side $B$ and then returning to $A$ can be in the inertial frame. The thick curve is the trajectory of the brane as viewed from side $B$, which is on the left side of the thick curve. The line segment $PQ$ denotes the part of the trajectory of the apparatus on side $B$ along which the apparatus is in free fall. The view from side $A$ has not been shown in this figure but it is of the same form as from side $B$.