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1. 2d (0, 2) gauge theories from branes: Recent progress in brane brick models

   https://doi.org/10.1142/S0217751X24460059  

   Franco, Sebastián (November 2024, International Journal of Modern Physics A)

   We discuss the realization of 2d (0,2) gauge theories in terms of branes focusing on Brane Brick Models, which are T-dual to D1-branes probing toric Calabi-Yau 4-folds. These brane setups fully encode the infinite class of 2d (0,2) quiver gauge theories on the worldvolume of the D1-branes and substantially streamline their connection to the probed geometries. We review various methods for efficiently generating Brane Brick Models. These algorithms are then used to construct 2d (0,2) gauge theories for the cones over all the smooth Fano 3-folds and two infinite families of Sasaki-Einstein 7-manifolds with known metrics. This note is based on the author’s talk at the Gauged Linear Sigma Models @ 30 conference at the Simons Center for Geometry and Physics. 

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2. Fano 3-folds, reflexive polytopes and brane brick models

   https://doi.org/10.1007/JHEP08(2022)008  

   Franco, Sebastián; Seong, Rak-Kyeong (August 2022, Journal of High Energy Physics)

   A bstract Reflexive polytopes in n dimensions have attracted much attention both in mathematics and theoretical physics due to their connection to Fano n -folds and mirror symmetry. This work focuses on the 18 regular reflexive polytopes corresponding to smooth Fano 3-folds. For the first time, we show that all 18 regular reflexive polytopes have corresponding 2 d (0 , 2) gauge theories realized by brane brick models. These 2 d gauge theories can be considered as the worldvolume theories of D1-branes probing the toric Calabi-Yau 4-singularities whose toric diagrams are given by the associated regular reflexive polytopes. The generators of the mesonic moduli space of the brane brick models are shown to form a lattice of generators due to the charges under the rank 3 mesonic flavor symmetry. It is shown that the lattice of generators is the exact polar dual reflexive polytope to the corresponding toric diagram of the brane brick model. This duality not only highlights the close relationship between the geometry and 2 d gauge theory, but also opens up pathways towards new discoveries in relation to reflexive polytopes and brane brick models. 

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3. Perturbative F-theory 10-brane and M-theory 5-brane

   https://doi.org/10.1007/JHEP11(2021)201  

   Hatsuda, Machiko; Siegel, Warren (November 2021, Journal of High Energy Physics)

   A bstract The exceptional symmetry is realized perturbatively in F-theory which is the manifest U-duality theory. The SO(5) U-duality symmetry acts on both the 16 space-time coordinates and the 10 worldvolume coordinates. Closure of the Virasoro algebra requires the Gauss law constraints on the worldvolume. This set of current algebras describes a F-theory 10-brane. The SO(5) duality symmetry is enlarged to the SO(6) symmetry in the Lagrangian formulation. We propose actions of the F-theory 10-brane with SO(5) and SO(6) symmetries. The gauge fields of the latter action are coset elements of SO(6)/SO(6; ℂ) which include both the SO(5)/SO(5; ℂ) spacetime backgrounds and the worldvolume backgrounds. The SO(5) current algebra obtained from the Pasti-Sorokin-Tonin M5-brane Lagrangian leads to the theory behind M-theory, namely F-theory. We also propose an action of the perturbative M-theory 5-brane obtained by sectioning the worldvolume of the F-theory 10-brane. 

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4. A non-abelian analogue of DBI from $$T \overline{T}$$

   https://doi.org/10.21468/SciPostPhys.8.4.052  

   Brennan, T. Daniel; Ferko, Christian; Sethi, Savdeep (January 2020, SciPost Physics)

   The Dirac action describes the physics of the Nambu-Goldstone scalarsfound on branes. The Born-Infeld action defines a non-linear theory ofelectrodynamics. The combined Dirac-Born-Infeld (DBI) action describesthe leading interactions supported on a single D-brane in string theory.We define a non-abelian analogue of DBI using the T\bar{T} T T ‾ deformation in two dimensions. The resulting quantum theory iscompatible with maximal supersymmetry and such theories are quiterare. 

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5. Geometries with mismatched branes

   https://doi.org/10.1007/JHEP09(2020)166  

   Karch, Andreas; Randall, Lisa (September 2020, Journal of High Energy Physics)

   A<sc>bstract</sc> We study Randall-Sundrum two brane setups with mismatched brane tensions. For the vacuum solutions, boundary conditions demand that the induced metric on each of the branes is either de Sitter, Anti-de Sitter, or Minkowski. For incompatible boundary conditions, the bulk metric is necessarily time-dependent. This introduces a new class of time-dependent solutions with the potential to address cosmological issues and provide alternatives to conventional inflationary (or contracting) scenarios. We take a first step in this paper toward such solutions. One important finding is that the resulting solutions can be very succinctly described in terms of an effective action involving only the induced metric on either one of the branes and the radion field. But the full geometry cannot necessarily be simply described with a single coordinate patch. We concentrate here on the time- dependent solutions but argue that supplemented with a brane stabilization mechanism one can potentially construct interesting cosmological models this way. This is true both with and without a brane stabilization mechanism. 

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