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Creation of D9-brane — anti-D9-brane Pairs from Hagedorn Transition of Closed Strings

Creation of D9-brane — anti-D9-brane Pairs from Hagedorn Transition of Closed Strings. Hokkaido Univ. Kenji Hotta. 1. Introduction. Hagedorn Temperature maximum temperature for perturbative strings A single energetic string captures most of the energy. Open String Gas on D9-brane

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Creation of D9-brane — anti-D9-brane Pairs from Hagedorn Transition of Closed Strings

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  1. Creation of D9-brane—anti-D9-brane Pairs from Hagedorn Transition of Closed Strings Hokkaido Univ. Kenji Hotta

  2. 1. Introduction • Hagedorn Temperature • maximum temperature for perturbative strings • A single energetic string captures most of the energy.

  3. Open String Gas on D9-brane • We need an infinite energy to reach. • is a `limiting temperature'. • Closed String Gas • We can reach by supplying a finite energy. • for (Matsubara Method) Winding modes in Euclidean time direction become tachyonic. Hagedorn Transition (Sathiapalan, Kogan, Atick-Witten) A phase transition takes place due to the condensation of tachyon fields. (stable minimum?)

  4. Dp-Dp pairsandNon-BPS Dp-branetype II • unstable at zero temperature • open string tachyon tachyon potential • finite temperature system of unstable branes • finite temperature effective potential (BSFT) • D9-D9 pairs and Non-BPS D9-branes become stable near the Hagedorn temperature. • Hotta  D9-D9 pairs • A phase transition occurs and Dp-Dp pairs become stable. •  Dp-Dp pairswith • No phase transition occurs.

  5. Thermodynamic Balance on D９-D９ Pair • (open string closed string) • open strings • We need an infinite energy to reach . closed strings • We can reach by supplying a finite energy. Energy flows from closed strings to open strings. Open strings dominate the total energy

  6. ‘Winding Tachyon’ CondensationAtick-Witten • For sphere world sheet does not contribute to free energy. • For sphere world sheet contributes to free energy. • insertion of ‘winding tachyon’ vertex • creation of a tiny hole in the world sheet which wraps around Euclidean time • boundary of a holeboundary of open string • on D９-D９ pair • Relation between two phase transitions? • From above arguments we conjecture that • D９-D９ Pairs are created by the Hagedorn transition of closed strings.

  7. Contents • Introduction  • Hagedorn Transition • BSFT Approach • BCFT Approach • Conclusion and Discussion

  8. 2. Hagedorn Transition • Matsubara Method • Euclidean time with period • ideal closed string gas1-loop (torus world sheet) • Proper Time Form of Free Energy • GSO projection

  9. Dual-representation • ‘winding tachyon' in the Euclidean time direction

  10. 3. BSFT Approach • BSFT (Boundary String Field Theory) • solution of classical master eq. (superstring) • : effective action : 2-dim. partition function • Dp-Dp Pair • open string tachyon tachyon potential • Sen’s conjecture potential height=brane tension

  11. tree amplitude (up to two derivative terms) • 1-loop amplitude • Conformal invariance is broken by the boundary terms. • ambiguity in choosing the Weyl factors

  12. Cylinder Boundary Action Andreev-Oft • Both sides of the cylinder world sheet are treated on an equal footing. • 2-dim. 1-loop partition function • low energy part of • = 1-loop partition function derived from

  13. Free Energy of Open Strings on D9-D9 Pair

  14. Free Energy near the Closed String Vacuum • propagator of ‘winding tachyon’ if we ignore part • momentum 0 momentum conservation for Neumann direction

  15. 3. BCFT Approach • BCFT (Boundary Conformal Field Theory) • boundary action(non-BPS D9-brane) • Euclidean version of rolling tachyon • non-BPS D9-brane • closed string vacuum • Matsubara Formalism

  16. 1-loop Free Energy Sugawara • SU(2) current algebra

  17. Closed String Vacuum Case • propagator of 'winding tachyon‘ • (‘winding tachyon' become massless at the Hagedorn temperature.)

  18. 5. Conclusion and Discussion • BSFT Approach • 1-loop free energy of open strings on D9-D9 pair • similar to propagator of ‘winding tachyon‘ • of closed strings • BCFT Approach • 1-loop free energy of open strings on non-BPS D9-brane • propagator of `winding tachyon' (massless) • of closed strings

  19. Hagedorn Transition Creation of D9-D9 Pair? • higher loop free energy of open strings • 'tree level' free energy of closed strings with ‘winding tachyon' vertexes? • ambiguity in choosing the Weyl factors? • cf) BCFT with imaginary D-branes Gaiotto-Itzhaki-Rastelli • disk scattering amplitude with m closed string insertion • sphere amplitude with m+1 closed string insertion • Dilaton? • Atick-Witten • first order phase transition • Non-perturbative Calculation? • Matrix model (IKKT, BFSS), K-matrix Model

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