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Open Branes in Space-Time Non-Commutative Little String Theory

Troels Harmark

TL;DR

This paper proposes two six-dimensional, non-gravitational open-brane theories, the $(1,1)$ and $(2,0)$ Open Brane Little String Theories (OBLSTs), as decoupling limits of NS5-branes in near-critical RR backgrounds, yielding space-time non-commutativity and open strings or membranes in their spectra. It constructs their supergravity duals, analyzes phase structures and thermodynamics, and demonstrates a network of S- and T-dualities that connect these theories to 5+1 dimensional NCOS and OM theory, with a closed chain linking OM, NCOS, and LST via bound-state dualities. A key result is the T-duality between open membranes and open strings, establishing a bridge between OM theory and NCOS in higher dimensions and revealing how non-commutative open branes organize the dynamics of these six-dimensional theories. Overall, the work provides a unified framework tying together OM theory, NCOS theories, and Little String Theory through holographic duals and dualities, advancing our understanding of non-perturbative, non-gravitational string dynamics in space-time non-commutative settings.

Abstract

We conjecture the existence of two new non-gravitational six-dimensional string theories, defined as the decoupling limit of NS5-branes in the background of near-critical electrical two- and three-form RR fields. These theories are space-time non-commutative Little String Theories with open branes. The theory with (2,0) supersymmetry has an open membrane in the spectrum and reduces to OM theory at low energies. The theory with (1,1) supersymmetry has an open string in the spectrum and reduces to 5+1 dimensional NCOS theory for weak NCOS coupling and low energies. The theories are shown to be T-dual with the open membrane being T-dual to the open string. The theories therefore provide a connection between 5+1 dimensional NCOS theory and OM theory. We study the supergravity duals of these theories and we consider a chain of dualities that shows how the T-duality between the two theories is connected with the S-duality between 4+1 dimensional NCOS theory and OM theory.

Open Branes in Space-Time Non-Commutative Little String Theory

TL;DR

This paper proposes two six-dimensional, non-gravitational open-brane theories, the and Open Brane Little String Theories (OBLSTs), as decoupling limits of NS5-branes in near-critical RR backgrounds, yielding space-time non-commutativity and open strings or membranes in their spectra. It constructs their supergravity duals, analyzes phase structures and thermodynamics, and demonstrates a network of S- and T-dualities that connect these theories to 5+1 dimensional NCOS and OM theory, with a closed chain linking OM, NCOS, and LST via bound-state dualities. A key result is the T-duality between open membranes and open strings, establishing a bridge between OM theory and NCOS in higher dimensions and revealing how non-commutative open branes organize the dynamics of these six-dimensional theories. Overall, the work provides a unified framework tying together OM theory, NCOS theories, and Little String Theory through holographic duals and dualities, advancing our understanding of non-perturbative, non-gravitational string dynamics in space-time non-commutative settings.

Abstract

We conjecture the existence of two new non-gravitational six-dimensional string theories, defined as the decoupling limit of NS5-branes in the background of near-critical electrical two- and three-form RR fields. These theories are space-time non-commutative Little String Theories with open branes. The theory with (2,0) supersymmetry has an open membrane in the spectrum and reduces to OM theory at low energies. The theory with (1,1) supersymmetry has an open string in the spectrum and reduces to 5+1 dimensional NCOS theory for weak NCOS coupling and low energies. The theories are shown to be T-dual with the open membrane being T-dual to the open string. The theories therefore provide a connection between 5+1 dimensional NCOS theory and OM theory. We study the supergravity duals of these theories and we consider a chain of dualities that shows how the T-duality between the two theories is connected with the S-duality between 4+1 dimensional NCOS theory and OM theory.

Paper Structure

This paper contains 18 sections, 106 equations, 10 figures.

Table of Contents

  1. Introduction
  2. $(1,1)$ OBLST and $D=5+1$ NCOS theory
  3. Introduction to $(1,1)$ OBLST
  4. The F1-D5 and D1-NS5 bound states
  5. Supergravity description of $(1,1)$ OBLST
  6. Branes in $(1,1)$ OBLST
  7. Supergravity dual of OM theory
  8. The M2-M5 and F1-D4 bound states
  9. Near-horizon limit of OM theory from $D=4+1$ NCOS
  10. Phase structure of OM and $D=4+1$ NCOS theory
  11. $(2,0)$ OBLST and OM theory
  12. Introduction to $(2,0)$ OBLST
  13. D2-NS5 bound state from M2-M5 on a transverse circle
  14. Supergravity dual of $(2,0)$ OBLST
  15. T-duality on an electric circle: From open membranes to open strings
  16. ...and 3 more sections

Figures (10)

  • Figure 1: Phase diagram for $(1,1)$ OBLST with $1/N \ll \tilde{g} \ll 1$.
  • Figure 2: Phase diagram for $(1,1)$ OBLST with $\tilde{g} \gg 1$.
  • Figure 3: Phase diagram for $(1,1)$ OBLST with $\tilde{g} \ll 1/N$.
  • Figure 4: Phase diagram of OM theory.
  • Figure 5: Phase diagram for $D=4+1$ NCOS with $1/N \ll \tilde{g} \ll 1$.
  • ...and 5 more figures