scholarly journals S-duality wall of SQCD from Toda braiding

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
B. Le Floch
Keyword(s):  
Field Theory ◽  
Gauge Theory ◽  
Domain Wall ◽  
Gauge Group ◽  
Domain Walls ◽  
Three Dimensional ◽  
Vertex Operators ◽  
Dual Operator ◽  
Yang Mills ◽  
Agt Correspondence

Abstract Exact field theory dualities can be implemented by duality domain walls such that passing any operator through the interface maps it to the dual operator. This paper describes the S-duality wall of four-dimensional $$ \mathcal{N} $$ N = 2 SU(N) SQCD with 2N hypermultiplets in terms of fields on the defect, namely three-dimensional $$ \mathcal{N} $$ N = 2 SQCD with gauge group U(N − 1) and 2N flavours, with a monopole superpotential. The theory is self-dual under a duality found by Benini, Benvenuti and Pasquetti, in the same way that T[SU(N)] (the S-duality wall of $$ \mathcal{N} $$ N = 4 super Yang-Mills) is self-mirror. The domain-wall theory can also be realized as a limit of a USp(2N − 2) gauge theory; it reduces to known results for N = 2. The theory is found through the AGT correspondence by determining the braiding kernel of two semi-degenerate vertex operators in Toda CFT.

scholarly journals Domain walls in 4d $$ \mathcal{N} $$ = 1 SYM

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Diego Delmastro ◽  
Jaume Gomis
Keyword(s):  
Domain Wall ◽  
Domain Walls ◽  
Simons Theory ◽  
Partition Functions ◽  
Quantum Field Theories ◽  
Yang Mills ◽  
Stable Domain ◽  
Coxeter Number ◽  
Topological Quantum ◽  
Simply Connected

Abstract 4d$$ \mathcal{N} $$ N = 1 super Yang-Mills (SYM) with simply connected gauge group G has h gapped vacua arising from the spontaneously broken discrete R-symmetry, where h is the dual Coxeter number of G. Therefore, the theory admits stable domain walls interpolating between any two vacua, but it is a nonperturbative problem to determine the low energy theory on the domain wall. We put forward an explicit answer to this question for all the domain walls for G = SU(N), Sp(N), Spin(N) and G2, and for the minimal domain wall connecting neighboring vacua for arbitrary G. We propose that the domain wall theories support specific nontrivial topological quantum field theories (TQFTs), which include the Chern-Simons theory proposed long ago by Acharya-Vafa for SU(N). We provide nontrivial evidence for our proposals by exactly matching renormalization group invariant partition functions twisted by global symmetries of SYM computed in the ultraviolet with those computed in our proposed infrared TQFTs. A crucial element in this matching is constructing the Hilbert space of spin TQFTs, that is, theories that depend on the spin structure of spacetime and admit fermionic states — a subject we delve into in some detail.

scholarly journals Toward AGT for Parabolic Sheaves

2020 ◽  
Author(s):  
Andrei Neguţ
Keyword(s):  
Field Theory ◽  
Gauge Theory ◽  
Conformal Field Theory ◽  
Moduli Spaces ◽  
Type A ◽  
Conformal Field ◽  
Toroidal Algebra ◽  
Agt Correspondence ◽  
K Theory ◽  
The Ideal

Abstract We construct explicit elements $W_{ij}^k$ in (a completion of) the shifted quantum toroidal algebra of type $A$ and show that these elements act by 0 on the $K$-theory of moduli spaces of parabolic sheaves. We expect that the quotient of the shifted quantum toroidal algebra by the ideal generated by the elements $W_{ij}^k$ will be related to $q$-deformed $W$-algebras of type $A$ for arbitrary nilpotent, which would imply a $q$-deformed version of the Alday-Gaiotto-Tachikawa (AGT) correspondence between gauge theory with surface operators and conformal field theory.

scholarly journals New soliton solutions of anti-self-dual Yang-Mills equations

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Masashi Hamanaka ◽  
Shan-Chi Huang
Keyword(s):  
Gauge Group ◽  
Darboux Transformation ◽  
Domain Walls ◽  
Soliton Solutions ◽  
Real Space ◽  
Explicit Calculation ◽  
Yang Mills ◽  
Action Density ◽  
New Type ◽  
Exact Soliton Solutions

Abstract We study exact soliton solutions of anti-self-dual Yang-Mills equations for G = GL(2) in four-dimensional spaces with the Euclidean, Minkowski and Ultrahyperbolic signatures and construct special kinds of one-soliton solutions whose action density TrFμνFμν can be real-valued. These solitons are shown to be new type of domain walls in four dimension by explicit calculation of the real-valued action density. Our results are successful applications of the Darboux transformation developed by Nimmo, Gilson and Ohta. More surprisingly, integration of these action densities over the four-dimensional spaces are suggested to be not infinity but zero. Furthermore, whether gauge group G = U(2) can be realized on our solition solutions or not is also discussed on each real space.

Self-duality in four-dimensional Riemannian geometry

1978 ◽  
Vol 362 (1711) ◽  
pp. 425-461 ◽  
Keyword(s):  
Gauge Group ◽  
Riemannian Geometry ◽  
Complex Analysis ◽  
Three Dimensional ◽  
The Self ◽  
Full Detail ◽  
Yang Mills ◽  
Self Duality ◽  
Compact Gauge Group

We present a self-contained account of the ideas of R. Penrose connecting four-dimensional Riemannian geometry with three-dimensional complex analysis. In particular we apply this to the self-dual Yang-Mills equations in Euclidean 4-space and compute the number of moduli for any compact gauge group. Results previously announced are treated with full detail and extended in a number of directions.

scholarly journals GEOMETRY OF ORIENTIFOLDS WITH NS–NS B FLUX

2000 ◽  
Vol 15 (20) ◽  
pp. 3113-3196 ◽  
Author(s):  
ZURAB KAKUSHADZE
Keyword(s):  
Field Theory ◽  
Conformal Field Theory ◽  
Gauge Symmetry ◽  
Fixed Points ◽  
Gauge Group ◽  
Qualitative Difference ◽  
Open String ◽  
Vertex Operators ◽  
Rank Reduction ◽  
Conformal Field

We discuss geometry underlying orientifolds with nontrivial NS–NS B flux. If D-branes wrap a torus with B flux the rank of the gauge group is reduced due to noncommuting Wilson lines whose presence is implied by the B flux. In the case of c-branes transverse to a torus with B flux the rank reduction is due to a smaller number of D-branes required by tadpole cancellation conditions in the presence of B flux as some of the orientifold planes now have the opposite orientifold projection. We point out that T duality in the presence of B flux is more subtle than in the case with trivial B flux, and it is precisely consistent with the qualitative difference between the aforementioned two setups. In the case where both types of branes are present, the states in the mixed (e.g. 59) open string sectors come with a nontrivial multiplicity, which we relate to a discrete gauge symmetry due to nonzero B flux, and construct vertex operators for the mixed sector states. Using these results we revisit K3 orientifolds with B flux (where K3 is a T4/ZM orbifold) and point out various subtleties arising in some of these models. For instance, in the Z2 case the conformal field theory orbifold does not appear to be the consistent background for the corresponding orientifolds with B flux. This is related to the fact that nonzero B flux requires the presence of both O5-- as well as O5+-planes at various Z2 orbifold fixed points, which appears to be inconsistent with the presence of the twistedB flux in the conformal field theory orbifold. We also consider four-dimensional [Formula: see text] and [Formula: see text] supersymmetric orientifolds. We construct consistent four-dimensional models with B flux which do not suffer from difficulties encountered in the K3 cases.

Role of division algebra in seven-dimensional gauge theory

2015 ◽  
Vol 30 (10) ◽  
pp. 1550047
Author(s):  
Pushpa Kalauni ◽  
J. C. A. Barata
Keyword(s):  
Gauge Theory ◽  
Division Algebra ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Dimensional Vector ◽  
Vector Product ◽  
Yang Mills ◽  
Rotational Transformation

The algebra of octonions 𝕆 forms the largest normed division algebra over the real numbers ℝ, complex numbers ℂ and quaternions ℍ. The usual three-dimensional vector product is given by quaternions, while octonions produce seven-dimensional vector product. Thus, octonionic algebra is closely related to the seven-dimensional algebra, therefore one can extend generalization of rotations in three dimensions to seven dimensions using octonions. An explicit algebraic description of octonions has been given to describe rotational transformation in seven-dimensional space. We have also constructed a gauge theory based on non-associative algebra to discuss Yang–Mills theory and field equation in seven-dimensional space.

scholarly journals Interconversion of multiferroic domains and domain walls

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
E. Hassanpour ◽  
M. C. Weber ◽  
Y. Zemp ◽  
L. Kuerten ◽  
A. Bortis ◽  
...  
Keyword(s):  
Domain Wall ◽  
Physical Properties ◽  
Domain Walls ◽  
Three Dimensional ◽  
Topological Defects ◽  
Long Range Order ◽  
Two Dimensional ◽  
Domain Structures ◽  
Topological Singularities ◽  
Ordered State

AbstractSystems with long-range order like ferromagnetism or ferroelectricity exhibit uniform, yet differently oriented three-dimensional regions called domains that are separated by two-dimensional topological defects termed domain walls. A change of the ordered state across a domain wall can lead to local non-bulk physical properties such as enhanced conductance or the promotion of unusual phases. Although highly desirable, controlled transfer of these properties between the bulk and the spatially confined walls is usually not possible. Here, we demonstrate this crossover by confining multiferroic Dy0.7Tb0.3FeO3 domains into multiferroic domain walls at an identified location within a non-multiferroic environment. This process is fully reversible; an applied magnetic or electric field controls the transformation. Aside from expanding the concept of multiferroic order, such interconversion can be key to addressing antiferromagnetic domain structures and topological singularities.

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