## Witten index and threshold bound states of D-branes.(English)Zbl 0925.58105

Summary: We consider the Witten index $$I= Tr(-1)^F$$ of SU(2) super Yang-Mills quantum mechanics (SYMQ) with $$N=16, 8, 4$$ supersymmetries. The theory governs the interactions between a pair of D-branes under various circumstances, and our goal is to count the number of the threshold bound states directly from the low-energy effective theory. String theory and M-theory have predicted that $$I=1$$ for $$N=16$$, which in fact forms an underlying hypothesis of the M(atrix)-theory formulation. Also the consistency of conifold transitions in type II theories is known to require $$I=0$$ for $$N=8$$ and 4. Here, the bulk contribution to I is computed explicitly, and for $$N=16, 8, 4$$, found to be $$5/4, 1/4, 1/4$$ respectively, suggesting a common defect contribution of $$-1/4$$. We illustrate how the defect term of $$-1/4$$ may arise in the SU(2) SYMQ by considering the effective dynamics along the asymptotic region.

### MSC:

 58J90 Applications of PDEs on manifolds 81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory 58J20 Index theory and related fixed-point theorems on manifolds 81T60 Supersymmetric field theories in quantum mechanics
Full Text:

### References:

 [1] J. Polchinski, TASI lectures on D-Branes, hep-th/9611050. [2] Witten, E., Nucl. phys. B, 460, 335, (1996) [3] Nahm, W., Phys. lett. B, 90, 413, (1980) [4] D.-E. Diaconescu, D-branes, monopoles and Nahm equations, hep-th/9608163 [5] M.R. Douglas and M. Li, D-brane realization of N = 2 super Yang-Mills theory in four dimensions, hep-th/9604041. [6] Intriligator, K.; Seiberg, N.; Hanany, A.; Witten, E., Phys. lett. B, Nucl. phys. B, 492, 152, (1997) [7] Witten, E.; Horava, P.; Witten, E., Nucl. phys. B, Nucl. phys. B, 460, 506, (1996) [8] Sen, A., Phys. rev. D, 54, 2964, (1996) [9] T. Banks, W. Fischler, S. Shenker and L. Susskind, M-theory as a matrix model: A conjecture, hep-th/9610043. · Zbl 1156.81433 [10] Strominger, A.; Greene, B.R.; Morrison, D.R.; Strominger, Andrew, Nucl. phys. B, Nucl. phys. B, 451, 109, (1995) [11] Bershadsky, M.; Vafa, C.; Sadov, V., Nucl. phys. B, 463, 420, (1996) [12] Claudson, M.; Halpern, M.B., Nucl. phys. B, 250, 689, (1985) [13] Danielsson, U.; Ferretti, G.; Sundborg, B., Int. J. mod. phys. A, 11, 5463, (1996), hep-th/9603081 [14] Kabat, D.; Pouliot, P.; Douglas, M.R.; Kabat, D.; Pouliot, P.; Shenker, S.H., Phys. rev. lett., Nucl. phys. B, 485, 85, (1997) [15] Lowe, D.A., Phys. lett. B, 403, 243, (1997) [16] Sethi, S.; Stern, M., Phys. lett. B, 398, 47, (1997) [17] S. Sethi and M. Stern, D-brane bound states redux, hep-th/9705046. · Zbl 0911.53052
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.