Exceptional N=3\mathcal N=3 theories

We present a new construction of four dimensional $\mathcal N=3$ theories, given by M5 branes wrapping a $T^2$ in an M-theory U-fold background. The resulting setup generalizes the one used in the usual class $\mathcal S$ construction of four dimensional theories by using an extra discrete symmetry on the M5 worldvolume. Together with the M-theory U-fold description of $(0,2)$ $E$-type six-dimensional SCFTs, this allows to construct new, exceptional, $\mathcal N=3$ theories.Comment: v2: Minor modifications, version to appear in JHE

Branes and Non‐Invertible Symmetries

=4 supersymmetric Yang-Mills theories with algebra(4N) and appropriate choices of global structure can have non-invertible symmetries. We identify the branes holographically dual to the non-invertible symmetries, and derive the fusion rules for the symmetries from the worldvolume dynamics on the branes

New N=1 dualities from orientifold transitions - Part II: String Theory

We present a string theoretical description, given in terms of branes and orientifolds wrapping vanishing cycles, of the dual pairs of gauge theories analyzed in 1210.7799. Based on the resulting construction we argue that the duality that we observe in field theory is inherited from S-duality of type IIB string theory. We analyze in detail the complex cone over the zeroth del Pezzo surface and discuss an infinite family of orbifolds of flat space. For the del Pezzo case we describe the system in terms of large volume objects, and show that in this language the duality can be understood from the strongly coupled behavior of the O7^+ plane, which we analyze using simple F-theory considerations. For all cases we also give a different argument based on the existence of appropriate torsional components of the 3-form flux lattice. Along the way we clarify some aspects of the description of orientifolds in the derived category of coherent sheaves, and in particular we discuss the important role played by exotic orientifolds - ordinary orientifolds composed with auto-equivalences of the category - when describing orientifolds of ordinary quiver gauge theories.Comment: 51 pages, 16 figures; v2: minor changes, added references, published versio

Dynamics of D-branes on local Calabi-Yau geometrics

Tesis Doctoral inédita leída en la Universidad Autónoma de Madrid, Facultad de Ciencias, Departamento de Física Teórica. Fecha de lectura: 14-03-200

Global structures from the infrared

Quantum field theories with identical local dynamics can admit different choices of global structure, leading to different partition functions and spectra of extended operators. Such choices can be reformulated in terms of a topological field theory in one dimension higher, the symmetry TFT. In this paper we show that this TFT can be reconstructed from a careful analysis of the infrared Coulomb-like phases. In particular, the TFT matches between the UV and the IR. This provides a purely field theoretical counterpart of several recent results obtained via geometric engineering in various string/M/F theory setups for theories in four and five dimensions that we confirm and extend.Comment: 26 pages, 4 figure

Non-geometric heterotic backgrounds and 6D SCFTs/LSTs

We study ${\mathcal N}=(1,0)$ six-dimensional theories living on defects of non-geometric backgrounds of the $E_8\times E_8$ and the $\text{Spin}(32)/{\mathbb Z}_2$ heterotic strings. Such configurations can be analyzed by dualizing to F-theory on elliptic K3-fibered non-compact Calabi-Yau threefolds. The majority of the resulting dual threefolds turn out to contain singularities which do not admit a crepant resolution. When the singularities can be resolved crepantly, the theories living on the defect are explicitly determined and reveal a form of duality in which distinct defects are described by the same IR fixed point. In particular, a subclass of non-geometric defects corresponds to SCFTs/LSTs arising from small heterotic instantons on ADE singularities.Comment: Slightly extended version of the proceedings prepared for the 'Workshop on Geometry and Physics,' November 2016, Ringberg Castle, Germany; 16 page

IIB flux non-commutativity and the global structure of field theories

We discuss the origin of the choice of global structure for six dimensional (2, 0) theories and their compactifications in terms of their realization from IIB string theory on ALE spaces. We find that the ambiguity in the choice of global structure on the field theory side can be traced back to a subtle effect that needs to be taken into account when specifying boundary conditions at infinity in the IIB orbifold, namely the known non-commutativity of RR fluxes in spaces with torsion. As an example, we show how the classification of N = 4 theories by Aharony, Seiberg and Tachikawa can be understood in terms of choices of boundary conditions for RR fields in IIB. Along the way we encounter a formula for the fractional instanton number of N = 4 ADE theories in terms of the torsional linking pairing for rational homology spheres. We also consider six-dimensional (1, 0) theories, clarifying the rules for determining commutators of flux operators for discrete 2-form symmetries. Finally, we analyze the issue of global structure for four dimensional theories in the presence of duality defects

Non-supersymmetric meta-stable vacua from brane configurations

We construct configurations of NS-, D4-, and D6-branes in type IIA string theory, realizing the recently discussed non-supersymmetric meta-stable minimum of 4d = 1 SU(Nc) super-Yang-Mills theories with massive flavors. We discuss their lift to M-theory and the mechanism of pseudo-moduli stabilization. We extend the construction to many other examples of meta-stable minima, including the SO/Sp theories, SU(Nc) with matter in two-index tensor representations, and to a chiral gauge theory