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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

Mikel Berasaluce-Gonz´ alez (JGU) On the physical realization of Seiberg dual phases in branes at singularities The String Theory Universe, Leuven, Septemb / 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.

Mikel Berasaluce-Gonz´ alez (JGU) On the physical realization of Seiberg dual phases in branes at singularities The String Theory Universe, Leuven, Septemb / 7

Case of interest: F0

Toric diagram: t x2 x3 x1 x4 Mori cone: x1 x2 x3 x4 t C1 1 1 −2 C2 1 1 −2 Newton polynomial: P(x, y) = a x + b y + cx + dy + e Mirror complex structure coordinates: z1 = ac e2 , z2 = bd e2

Quiver Locus

z1, z2 → ∞ and z1 z2 = e2πiθ

Mikel Berasaluce-Gonz´ alez (JGU) On the physical realization of Seiberg dual phases in branes at singularities The String Theory Universe, Leuven, Septemb / 7

Toric Phases of F0

Phase I Dimer 1 2 2 3 3 3 3 4 4 Mirror geometry Phase II Dimer 1 4 4 2 2 3 3 3 3 Mirror geometry

Figures taken from hep-th/0110028.

Mikel Berasaluce-Gonz´ alez (JGU) On the physical realization of Seiberg dual phases in branes at singularities The String Theory Universe, Leuven, Septemb / 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

Mikel Berasaluce-Gonz´ alez (JGU) On the physical realization of Seiberg dual phases in branes at singularities The String Theory Universe, Leuven, Septemb / 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 = e0.3i a = e0.15i a = 0 a = e−0.15i a = e0.3i

In all cases b = c = d = 1, e = 0. Therefore, the phase II will never be realized at weak gauge coupling.

Mikel Berasaluce-Gonz´ alez (JGU) On the physical realization of Seiberg dual phases in branes at singularities The String Theory Universe, Leuven, Septemb / 7

Conclusions and future directions

Conclusions

We have studied the physical realization of Seiberg dual theories in branes at singularities. In the F0 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 dP2 and dP3.

Mikel Berasaluce-Gonz´ alez (JGU) On the physical realization of Seiberg dual phases in branes at singularities The String Theory Universe, Leuven, Septemb / 7