Abstract
Utilizing the large N dual description of a metastable system of branes and anti-branes wrapping rigid homologous S^2's in a non-compact Calabi-Yau threefold, we study phase transitions induced by changing the positions of the S^2's. At leading order in 1/N the effective potential for this system is computed by the planar limit of an auxiliary matrix model. Beginning at the two loop correction, the degenerate vacuum energy density of the discrete confining vacua split, and a potential is generated for the axion. Changing the relative positions of the S^2's causes discrete jumps in the energetically preferred confining vacuum and can also obstruct direct brane/anti-brane annihilation processes. The branes must hop to nearby S^2's before annihilating, thus significantly increasing the lifetime of the corresponding non-supersymmetric vacua. We also speculate that misaligned metastable glueball phases may generate a repulsive inter-brane force which stabilizes the radial mode present in compact Calabi-Yau threefolds.
Highlights
Metastable vacua of supersymmetric string and field theories possess the attractive feature that in contrast to a generic non-supersymmetric system, the underlying supersymmetry of the theory often provides better control over the dynamics of the vacuum
Recent progress in finding non-supersymmetric metastable vacua in supersymmetric QCD-like field theories was achieved in [12] and subsequent string theory realizations of this work [13,14,15,16,17,18,19,20,21,22,23,24,25,26,27]. Combining these stringy insights with the dual closed string description of large N open string systems such as the AdS/CFT correspondence [28,29,30] and geometric transitions [1, 31, 32], it was shown in [6] that much of the rigid structure of N = 2 supersymmetry remains intact for metastable vacua in type IIB string theory given by D5-branes and anti-D5-branes wrapping distinct minimal size S2’s in a non-compact Calabi-Yau geometry of the form: y2 = W ′(x)2 + uv where W ′(x) = g(x − a1) · · · (x − an) is a polynomial of degree n, the variables x, y, u, v ∈ C and the minimal size S2’s are located at x = ai
The geometry of the closed string dual description is given by blowing down the S2 and introducing a complex deformation of equation (1) by a degree n − 1 polynomial in x: y2 = W ′(x)2 + fn−1(x) + uv
Summary
Metastable vacua of supersymmetric string and field theories possess the attractive feature that in contrast to a generic non-supersymmetric system, the underlying supersymmetry of the theory often provides better control over the dynamics of the vacuum. Recent progress in finding non-supersymmetric metastable vacua in supersymmetric QCD-like field theories was achieved in [12] and subsequent string theory realizations of this work [13,14,15,16,17,18,19,20,21,22,23,24,25,26,27] Combining these stringy insights with the dual closed string description of large N open string systems such as the AdS/CFT correspondence [28,29,30] and geometric transitions [1, 31, 32], it was shown in [6] that much of the rigid structure of N = 2 supersymmetry remains intact for metastable vacua in type IIB string theory given by D5-branes and anti-D5-branes wrapping distinct minimal size S2’s in a non-compact Calabi-Yau geometry of the form: y2 = W ′(x)2 + uv (1). A generic configuration of additional S2’s will typically obstruct a direct collision between the cuts supported by positive and negative flux Such obstructions can lead to phase transitions to non-Kahler geometries of the type found in [8].
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