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 BPS Quivers of Five-Dimensional SCFTs, Topological Strings and q-Painlevé Equations

2021 ◽  
Author(s):  
Giulio Bonelli ◽  
Fabrizio Del Monte ◽  
Alessandro Tanzini
Keyword(s):  
Topological String ◽  
Cluster Algebra ◽  
Painlevé Equations ◽  
Partition Functions ◽  
Quantum Field Theories ◽  
Particle Spectrum ◽  
Yang Mills ◽  
Painleve Equations ◽  
Rank One ◽  
Bilinear Equations

AbstractWe study the discrete flows generated by the symmetry group of the BPS quivers for Calabi–Yau geometries describing five-dimensional superconformal quantum field theories on a circle. These flows naturally describe the BPS particle spectrum of such theories and at the same time generate bilinear equations of q-difference type which, in the rank one case, are q-Painlevé equations. The solutions of these equations are shown to be given by grand canonical topological string partition functions which we identify with $$\tau $$ τ -functions of the cluster algebra associated to the quiver. We exemplify our construction in the case corresponding to five-dimensional SU(2) pure super Yang–Mills and $$N_f=2$$ N f = 2 on a circle.

scholarly journals THE RELATIONS BETWEEN GENERALIZED FIELDS AND SUPERFIELDS FORMALISMS OF THE BATALIN–VILKOVISKY METHOD OF QUANTIZATION

2004 ◽  
Vol 19 (14) ◽  
pp. 2339-2353 ◽  
Author(s):  
ÖMER F. DAYI
Keyword(s):  
General Solution ◽  
Master Equation ◽  
Gauge Theories ◽  
Relativistic Particle ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Yang Mills ◽  
Topological Quantum ◽  
Topological Quantum Field Theories

A general solution of the Batalin–Vilkovisky master equation was formulated in terms of generalized fields. Recently, a superfields approach of obtaining solutions of the Batalin–Vilkovisky master equation is also established. Superfields formalism is usually applied to topological quantum field theories. However, generalized fields method is suitable to find solutions of the Batalin–Vilkovisky master equation either for topological quantum field theories or the usual gauge theories like Yang–Mills theory. We show that by truncating some components of superfields with appropriate actions, generalized fields formalism of the usual gauge theories result. We demonstrate that for some topological quantum field theories and the relativistic particle both of the methods possess the same field contents and yield similar results. Inspired by the observed relations, we give the solution of the BV master equation for on-shell N=1 supersymmetric Yang–Mills theory utilizing superfields.

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 Non-unitary TQFTs from 3D $$ \mathcal{N} $$ = 4 rank 0 SCFTs

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Dongmin Gang ◽  
Sungjoon Kim ◽  
Kimyeong Lee ◽  
Myungbo Shim ◽  
Masahito Yamazaki
Keyword(s):  
Field Theories ◽  
Partition Functions ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Superconformal Field Theory ◽  
Three Sphere ◽  
Topological Quantum ◽  
S Matrix ◽  
Modular Data ◽  
Topological Theories

Abstract We propose a novel procedure of assigning a pair of non-unitary topological quantum field theories (TQFTs), TFT±[$$ \mathcal{T} $$ T rank 0], to a (2+1)D interacting $$ \mathcal{N} $$ N = 4 superconformal field theory (SCFT) $$ \mathcal{T} $$ T rank 0 of rank 0, i.e. having no Coulomb and Higgs branches. The topological theories arise from particular degenerate limits of the SCFT. Modular data of the non-unitary TQFTs are extracted from the supersymmetric partition functions in the degenerate limits. As a non-trivial dictionary, we propose that F = maxα (− log|$$ {S}_{0\alpha}^{\left(+\right)} $$ S 0 α + |) = maxα (− log|$$ {S}_{0\alpha}^{\left(-\right)} $$ S 0 α − |), where F is the round three-sphere free energy of $$ \mathcal{T} $$ T rank 0 and $$ {S}_{0\alpha}^{\left(\pm \right)} $$ S 0 α ± is the first column in the modular S-matrix of TFT±. From the dictionary, we derive the lower bound on F, F ≥ − log $$ \left(\sqrt{\frac{5-\sqrt{5}}{10}}\right) $$ 5 − 5 10 ≃ 0.642965, which holds for any rank 0 SCFT. The bound is saturated by the minimal $$ \mathcal{N} $$ N = 4 SCFT proposed by Gang-Yamazaki, whose associated topological theories are both the Lee-Yang TQFT. We explicitly work out the (rank 0 SCFT)/(non-unitary TQFTs) correspondence for infinitely many examples.

scholarly journals Supersymmetric domain walls in maximal 6D gauged supergravity I

2021 ◽  
Vol 81 (8) ◽  
Author(s):  
Parinya Karndumri ◽  
Patharadanai Nuchino
Keyword(s):  
Domain Wall ◽  
Large Class ◽  
Domain Walls ◽  
Global Symmetry ◽  
Five Dimensions ◽  
Gauge Groups ◽  
Yang Mills

AbstractWe find a large class of supersymmetric domain wall solutions from six-dimensional $$N=(2,2)$$ N = ( 2 , 2 ) gauged supergravity with various gauge groups. In general, the embedding tensor lives in $${{\mathbf {144}}}_c$$ 144 c representation of the global symmetry SO(5, 5). We explicitly construct the embedding tensors in $${{\mathbf {15}}}^{-1}$$ 15 - 1 and $$\overline{{\mathbf {40}}}^{-1}$$ 40 ¯ - 1 representations of $$GL(5)\sim {\mathbb {R}}^+\times SL(5)\subset SO(5,5)$$ G L ( 5 ) ∼ R + × S L ( 5 ) ⊂ S O ( 5 , 5 ) leading to $$CSO(p,q,5-p-q)$$ C S O ( p , q , 5 - p - q ) and $$CSO(p,q,4-p-q)\ltimes {\mathbb {R}}^4_{{\varvec{s}}}$$ C S O ( p , q , 4 - p - q ) ⋉ R s 4 gauge groups, respectively. These gaugings can be obtained from $$S^1$$ S 1 reductions of seven-dimensional gauged supergravity with $$CSO(p,q,5-p-q)$$ C S O ( p , q , 5 - p - q ) and $$CSO(p,q,4-p-q)$$ C S O ( p , q , 4 - p - q ) gauge groups. As in seven dimensions, we find half-supersymmetric domain walls for purely magnetic or purely electric gaugings with the embedding tensors in $${{\mathbf {15}}}^{-1}$$ 15 - 1 or $$\overline{{\mathbf {40}}}^{-1}$$ 40 ¯ - 1 representations, respectively. In addition, for dyonic gauge groups with the embedding tensors in both $${{\mathbf {15}}}^{-1}$$ 15 - 1 and $$\overline{{\mathbf {40}}}^{-1}$$ 40 ¯ - 1 representations, the domain walls turn out to be $$\frac{1}{4}$$ 1 4 -supersymmetric as in the seven-dimensional analogue. By the DW/QFT duality, these solutions are dual to maximal and half-maximal super Yang–Mills theories in five dimensions. All of the solutions can be uplifted to seven dimensions and further embedded in type IIB or M-theories by the well-known consistent truncation of the seven-dimensional $$N=4$$ N = 4 gauged supergravity.

scholarly journals Five-dimensional gauge theories on spheres with negative couplings

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Joseph A. Minahan ◽  
Anton Nedelin
Keyword(s):  
Gauge Theory ◽  
Gauge Theories ◽  
Simons Theory ◽  
Partition Functions ◽  
Yang Mills ◽  
Hooft Coupling ◽  
Instanton Contribution ◽  
Sphere Radius ◽  
Supersymmetric Gauge ◽  
Chern Simons

Abstract We consider supersymmetric gauge theories on S5 with a negative Yang-Mills coupling in their large N limits. Using localization we compute the partition functions and show that the pure SU(N) gauge theory descends to an SU(N/2)+N/2× SU(N/2)−N/2× SU(2) Chern-Simons gauge theory as the inverse ’t Hooft coupling is taken to negative infinity for N even. The Yang-Mills coupling of the SU(N/2)±N/2 is positive and infinite, while that on the SU(2) goes to zero. We also show that the odd N case has somewhat different behavior. We then study the SU(N/2)N/2 pure Chern-Simons theory. While the eigenvalue density is only found numerically, we show that its width equals 1 in units of the inverse sphere radius, which allows us to find the leading correction to the free energy when turning on the Yang-Mills term. We then consider USp(2N) theories with an antisymmetric hypermultiplet and Nf< 8 fundamental hypermultiplets and carry out a similar analysis. Along the way we show that the one-instanton contribution to the partition function remains exponentially suppressed at negative coupling for the SU(N) theories in the large N limit.

scholarly journals ON GENERALIZED SELF-DUALITY EQUATIONS TOWARDS SUPERSYMMETRIC QUANTUM FIELD THEORIES OF FORMS

1998 ◽  
Vol 13 (14) ◽  
pp. 1115-1132 ◽  
Author(s):  
LAURENT BAULIEU ◽  
CÉLINE LAROCHE
Keyword(s):  
The Self ◽  
Field Theories ◽  
Gauge Fields ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Time Dimension ◽  
Yang Mills ◽  
Self Duality ◽  
Topological Quantum ◽  
Gauge Functions

We classify possible "self-duality" equations for p-form gauge fields in space–time dimension up to D=16, generalizing the pioneering work of Corrigan et al. (1982) on Yang–Mills fields (p=1) in 4<D≤8. We impose two crucial requirements. First, there should exist a 2(p+1)-form T-invariant under a subgroup H of SO D. Second, the representation for the SO D curvature of the gauge field must decompose under H in a relevant way. When these criteria are fulfilled, the "self-duality" equations can be candidates of gauge functions for SO D-covariant and H-invariant topological quantum field theories. Intriguing possibilities occur for D≥10 for various p-form gauge fields.

Quantum theories and geometric topology: A chapter in physical mathematics

2014 ◽  
Vol 11 (07) ◽  
pp. 1460024
Author(s):  
Kishore Marathe
Keyword(s):  
Topological String ◽  
Geometric Topology ◽  
Simons Theory ◽  
Quantum Field Theories ◽  
Quantum Theories ◽  
Low Dimensional Topology ◽  
Black Hole Radiation ◽  
Topological Quantum ◽  
Low Dimensional ◽  
String Amplitudes

In recent years, the interaction between geometric topology and classical and quantum field theories has attracted a great deal of attention from both the mathematicians and physicists. We discuss some topics from low-dimensional topology where this has led to new viewpoints as well as new results. They include categorification of knot polynomials and a special case of the gauge theory to string theory correspondence in the Euclidean version of the theories, where exact results are available. We show how the Witten–Reshetikhin–Turaev invariant in SU (n) Chern–Simons theory on S3 is related via conifold transition to the all-genus generating function of the topological string amplitudes on a Calabi–Yau manifold. This result can be thought of as an interpretation of TQFT as topological quantum gravity (TQG). After a brief discussion of Perelman's work on the geometrization conjecture and its relation to gravity, we comment on some recent work on black hole radiation and its relation to mock moonshine.

scholarly journals Confinement on ℝ3 × 𝕊1 and double-string collapse

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Mathew W. Bub ◽  
Erich Poppitz ◽  
Samuel S.Y. Wong
Keyword(s):  
Domain Wall ◽  
Flux Tube ◽  
Bound States ◽  
Scaling Laws ◽  
Domain Walls ◽  
Flux Line ◽  
Yang Mills ◽  
Confining Unit ◽  
Semiclassical Regime

Abstract We study confining strings in $$ \mathcal{N} $$ N = 1 supersymmetric SU(Nc) Yang-Mills theory in the semiclassical regime on ℝ1,2× 𝕊1. Static quarks are expected to be confined by double strings composed of two domain walls — which are lines in ℝ2 — rather than by a single flux tube. Each domain wall carries part of the quarks’ chromoelectric flux. We numerically study this mechanism and find that double-string confinement holds for strings of all N-alities, except for those between fundamental quarks. We show that, for Nc≥ 5, the two domain walls confining unit N-ality quarks attract and form non-BPS bound states, collapsing to a single flux line. We determine the N-ality dependence of the string tensions for 2 ≤ Nc≤ 10. Compared to known scaling laws, we find a weaker, almost flat N-ality dependence, which is qualitatively explained by the properties of BPS domain walls. We also quantitatively study the behavior of confining strings upon increasing the 𝕊1 size by including the effect of virtual “W-bosons” and show that the qualitative features of double-string confinement persist.

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