Phase structure of D-brane gauge theories and toric duality (original) (raw)

MIT-CTP-3646 , CERN-PH-TH / 2005-084 , HUTP-05 / A 0027 Gauge Theories from Toric Geometry and Brane

2005

We provide a general set of rules for extracting the data defining a quiver gauge theory from a given toric Calabi–Yau singularity. Our method combines information from the geometry and topology of Sasaki–Einstein manifolds, AdS/CFT, dimers, and brane tilings. We explain how the field content, quantum numbers, and superpotential of a superconformal gauge theory on D3–branes probing a toric Calabi–Yau singularity can be deduced. The infinite family of toric singularities with known horizon Sasaki–Einstein manifolds L is used to illustrate these ideas. We construct the corresponding quiver gauge theories, which may be fully specified by giving a tiling of the plane by hexagons with certain gluing rules. As checks of this construction, we perform a-maximisation as well as Z-minimisation to compute the exact R-charges of an arbitrary such quiver. We also examine a number of examples in detail, including the infinite subfamily L, whose smallest member is the Suspended Pinch Point.

M5-branes, toric diagrams and gauge theory duality

Journal of High Energy Physics, 2012

In this article we explore the duality between the low energy effective theory of fivedimensional N = 1 SU (N) M −1 and SU (M) N −1 linear quiver gauge theories compactified on S 1. The theories we study are the five-dimensional uplifts of four-dimensional superconformal linear quivers. We study this duality by comparing the Seiberg-Witten curves and the Nekrasov partition functions of the two dual theories. The Seiberg-Witten curves are obtained by minimizing the worldvolume of an M5-brane with nontrivial geometry. Nekrasov partition functions are computed using topological string theory. The result of our study is a map between the gauge theory parameters, i.e., Coulomb moduli, masses and UV coupling constants, of the two dual theories. Apart from the obvious physical interest, this duality also leads to compelling mathematical identities. Through the AGTW conjecture these five-dimentional gauge theories are related to q-deformed Liouville and Toda SCFTs in two-dimensions. The duality we study implies the relations between Liouville and Toda correlation functions through the map we derive.

Superconformal D-branes and moduli spaces

2003

The on-going quest for a single theory that describes all the forces of nature has led to the discovery of string theory. This is the only known theory that successfully unifies gravity with the electroweak and strong forces. It postulates that the fundamental building blocks of nature are strings, and that all particles arise as different excitations of strings. This theory is still poorly understood, especially at strong coupling, but progress is being made all the time. One breakthrough came with the discovery of extended objects called D-branes, which have proved crucial in probing the strong-coupling regime. They are instrumental in realising dualities (equivalences) between different limits of string theory.

Towards M2-brane theories for generic toric singularities

Journal of High Energy Physics, 2008

We construct several examples of (2+1) dimensional N=2 supersymmetric Chern-Simons theories, whose moduli space is given by non-compact toric Calabi-Yau four-folds, which are not derivable from any (3+1) dimensional CFT. One such example is the gauge theory associated with the cone over Q^{111}. For several examples, we explicitly confirm the matter content, superpotential interactions and RG flows suggested by crystal models. Our results provide additional support to the idea that crystal models are relevant for describing the structure of these CFTs.

D-branes at toric singularities: model building, Yukawa couplings and flavour physics

Journal of High Energy Physics, 2010

We discuss general properties of D-brane model building at toric singularities. Using dimer techniques to obtain the gauge theory from the structure of the singularity, we extract results on the matter sector and superpotential of the corresponding gauge theory. We show that the number of families in toric phases is always less than or equal to three, with a unique exception being the zeroth Hirzebruch surface. With the physical input of three generations we find that the lightest family of quarks is massless and the masses of the other two can be hierarchically separated. We compute the CKM matrix for explicit models in this setting and find the singularities possess sufficient structure to allow for realistic mixing between generations and CP violation. 6 1 2 3

Gauge fields on tori and T-duality

Physics Letters B, 2003

We discuss gauge fields on tori in diverse dimensions, mainly in two and four dimensions. We construct various explicit gauge fields which have some topological charges and find the Dirac zero modes in the background of the gauge fields. By using the zero mode, we give new gauge fields on the dual torus, which is a gauge theoretical description of T-duality transformation of the corresponding D-brane systems including DD systems. From the transformation, we can easily see the duality expected from the index theorem. It is also mentioned that, for each topological charges, the corresponding constant curvature bundle can be constructed and their duality transformation can be performed in terms of Heisenberg modules.

The Phase Transitions and the Moduli Space of Particles from D- Brane

The study of the birth of the Universe is closely related to the study of phase transitions in high-energy physics implemented in the framework of the theory of derived categories. Using the theory of D-branes and superstrings, the properties of the C 3 ∕Z 3 orbifold as a space of extra dimensions were studied. In the framework of the criterion of stability of the D-brane as bound state of fractional branes O P2 and O P2 (-3) the impossibility of phase transition of one sheaf into another one was shown. The category of distinguished triangles with objects-McKay quivers and morphism between them-Ext q (A,B)-group was used for the calculation of the number of vibrational modes of the string presented by Poincare supergravity with N = 4.

The dynamics of D3-brane dyons and toric hyper-Kähler manifold

Nuclear Physics B, 1999

We find the dyonic worldvolume solitons due to parallel (p,q) strings ending on a D-3-brane. These solutions preserve 1/4 of bulk supersymmetry. Then we investigate the scattering of well-separated dyons and find that their moduli space is a toric hyper-Kähler manifold. In addition, we present the worldvolume solitons of the D-3-brane which are related by duality to the M-theory configuration of two orthogonal membranes ending on a M-5-brane. We show that these solitons preserve 1/8 of supersymmetry and compute their effective action.

Gauge theories from toric geometry and brane tilings

Journal of High Energy Physics, 2006

We provide a general set of rules for extracting the data defining a quiver gauge theory from a given toric Calabi-Yau singularity. Our method combines information from the geometry and topology of Sasaki-Einstein manifolds, AdS/CFT, dimers, and brane tilings. We explain how the field content, quantum numbers, and superpotential of a superconformal gauge theory on D3-branes probing a toric Calabi-Yau singularity can be deduced. The infinite family of toric singularities with known horizon Sasaki-Einstein manifolds L^{a,b,c} is used to illustrate these ideas. We construct the corresponding quiver gauge theories, which may be fully specified by giving a tiling of the plane by hexagons with certain gluing rules. As checks of this construction, we perform a-maximisation as well as Z-minimisation to compute the exact R-charges of an arbitrary such quiver. We also examine a number of examples in detail, including the infinite subfamily L^{a,b,a}, whose smallest member is the Suspended Pinch Point.