On the physical realization of Seiberg dual phases in branes at - PowerPoint PPT Presentation

On the physical realization of Seiberg dual phases in branes at singularities Mikel Berasaluce-Gonz´ alez Johannes Gutenberg Universit¨ at Based on: Ongoing work with I˜ naki Garc´ ıa-Etxebarria and Ben Heidenreich The String Theory Universe, Leuven, September 8, 2015 The String Theory Universe, Leuven, Septemb Mikel Berasaluce-Gonz´ alez (JGU) On the physical realization of Seiberg dual phases in branes at singularities / 7

Introduction Seiberg duality is an important aspect of N = 1 supersymmetric gauge theory. In string theory, Seiberg duality is often realized by supersymmetric deformations of systems of branes that induce irrelevant deformations of the low energy EFT. In the context of chiral quiver theories, the algebraic (chiral ring) content of Seiberg duality can be understood at the level of topological string theory. [Berenstein, Douglas; hep-th/0207027] An interesting question is finding to what extend the same occurs in the full string theory, once we take into account BPS conditions for the brane system. In particular, we will be interested in the case of D-branes sitting on a singularity inside a Calabi-Yau manifold. The quiver gauge theory will be physically realized when the periods characterizing the central charges for the associated fractional branes are aligned. [e.g. hep-th/0405134] Note: we will only consider the K¨ ahler moduli space at weak coupling. Method Compute the periods and see where, at Vol → 0, all arguments are the same (quiver locus). Look to the mirror geometry to see which phases are being realized. The String Theory Universe, Leuven, Septemb Mikel Berasaluce-Gonz´ alez (JGU) On the physical realization of Seiberg dual phases in branes at singularities / 7

Case of interest: F 0 Mori cone: Newton polynomial: Toric diagram: x 3 x 1 x 2 x 3 x 4 t P ( x , y ) = a x + b y + cx + dy + e C 1 0 1 0 1 − 2 t C 2 1 0 1 0 − 2 x 4 x 2 Mirror complex structure coordinates: z 1 = ac z 2 = bd x 1 e 2 , e 2 Quiver Locus z 1 = e 2 π i θ z 1 , z 2 → ∞ and z 2 The String Theory Universe, Leuven, Septemb Mikel Berasaluce-Gonz´ alez (JGU) On the physical realization of Seiberg dual phases in branes at singularities / 7

Toric Phases of F 0 Phase I Phase II Dimer Dimer 3 3 3 4 3 4 2 1 2 2 1 2 4 3 4 3 3 3 Mirror geometry Mirror geometry Figures taken from hep-th/0110028. The String Theory Universe, Leuven, Septemb Mikel Berasaluce-Gonz´ alez (JGU) On the physical realization of Seiberg dual phases in branes at singularities / 7

Physical realization of the phases. Phase I Phase I is physically realized. Take e.g. b = c = d = 1, a = i and e = 0 in the Newton polynomial. The mirror is The String Theory Universe, Leuven, Septemb Mikel Berasaluce-Gonz´ alez (JGU) On the physical realization of Seiberg dual phases in branes at singularities / 7

Physical realization of the phases. Phase II We can obtain the phase II if one of the singularities in the mirror goes through the origin. However, it can be shown that there are precisely two branes becomming massless simultaneously. a = e 0 . 3 i a = e 0 . 15 i a = e − 0 . 15 i a = e 0 . 3 i a = 0 In all cases b = c = d = 1, e = 0. Therefore, the phase II will never be realized at weak gauge coupling. The String Theory Universe, Leuven, Septemb Mikel Berasaluce-Gonz´ alez (JGU) On the physical realization of Seiberg dual phases in branes at singularities / 7

Conclusions and future directions Conclusions We have studied the physical realization of Seiberg dual theories in branes at singularities. In the F 0 case, only phase I can be realized at weak gauge coupling. Future directions Extend the analysis to other cases with Seiberg duals phases which are also toric duals like the complex cones over dP 2 and dP 3 . The String Theory Universe, Leuven, Septemb Mikel Berasaluce-Gonz´ alez (JGU) On the physical realization of Seiberg dual phases in branes at singularities / 7