Six-dimensional Origin of $\mathcal{N}=4$ SYM with Duality Defects

Assel, Benjamin; Schäfer-Nameki, Sakura

doi:10.1007/JHEP12(2016)058

Article
Report number	arXiv:1610.03663 ; CERN-TH-2016-216 ; CERN-TH-2016-216
Title	Six-dimensional Origin of $\mathcal{N}=4$ SYM with Duality Defects
Author(s)	Assel, Benjamin (CERN ; King's Coll. London, Dept. Math) ; Schäfer-Nameki, Sakura (Oxford U., Inst. Math. ; King's Coll. London, Dept. Math)
Publication	2016-12-14
Imprint	12 Oct 2016
Number of pages	62
Note	Comments: 62 pages, 4 figures 62 pages, 4 figures
In:	JHEP 12 (2016) 058
DOI	10.1007/JHEP12(2016)058
Subject category	Particle Physics - Theory
Abstract	We study the topologically twisted compactification of the 6d $(2,0)$ M5-brane theory on an elliptically fibered K\"ahler three-fold preserving two supercharges. We show that upon reducing on the elliptic fiber, the 4d theory is $\mathcal{N}=4$ Super-Yang Mills, with varying complexified coupling $\tau$, in the presence of defects. For abelian gauge group this agrees with the so-called duality twisted theory, and we determine a non-abelian generalization to $U(N)$. When the elliptic fibration is singular, the 4d theory contains 3d walls (along the branch-cuts of $\tau$) and 2d surface defects, around which the 4d theory undergoes $SL(2,\mathbb{Z})$ duality transformations. Such duality defects carry chiral fields, which from the 6d point of view arise as modes of the two-form $B$ in the tensor multiplet. Each duality defect has a flavor symmetry associated to it, which is encoded in the structure of the singular elliptic fiber above the defect. Generically 2d surface defects will intersect in points in 4d, where there is an enhanced flavor symmetry. The 6d point of view provides a complete characterization of this 4d-3d-2d-0d `Matroshka'-defect configuration.
Copyright/License	arXiv nonexclusive-distrib. 1.0 preprint: © 2016-2025 CERN (License: CC-BY-4.0) publication: © 2016-2025 The Author(s) (License: CC-BY-4.0), sponsored by SCOAP³

$Setup of 4d theory on $B_2$ with local coordinates $z_1$ and $z_2$. The curve $\mathcal{C}$ is given by $z_1=0$, and the wall $W^{\gamma}$ by $\theta_1 =0$, where $\theta_1$ is the angular coordinate of $z_1$. As one crosses the branch-cut $W^\gamma$, the coupling undergoes an $SL(2,\mathbb{Z})$ monodromy $\gamma$.$ $Schematics of the setup: The total space is the elliptically fibered Calabi-Yau four-fold $X_4$, with base three-fold $M$. The restriction of the fibration to the subspace $B \subset M$ results in the elliptic three-fold $Y_3$, which will be wrapped by the M5-brane. The fiber becomes singular above the locus $\Delta\subset M$, which intersects $B$ in (a collection of) curve(s) $\mathcal{C}$.$ Show more plots

Corresponding record in: Inspire

Back to search

Записът е създаден на 2016-10-13, последна промяна на 2024-08-29

Подобни записи

Article from SCOAP3: