scholarly journals Instantons and Bows for the Classical Groups

2020 ◽  
Author(s):  
Sergey A Cherkis ◽  
Jacques Hurtubise
Keyword(s):  
Gauge Theory ◽  
Moduli Space ◽  
Finite Subgroup ◽  
Structure Group ◽  
Classical Groups ◽  
Coulomb Branch ◽  
Quiver Gauge Theory ◽  
Instanton Bundles ◽  
Similar Classification

Abstract The construction of Atiyah, Drinfeld, Hitchin and Manin provided complete description of all instantons on Euclidean four-space. It was extended by Kronheimer and Nakajima to instantons on ALE spaces, resolutions of orbifolds $\mathbb{R}^4/\Gamma$ by a finite subgroup Γ⊂SU(2). We consider a similar classification, in the holomorphic context, of instantons on some of the next spaces in the hierarchy, the ALF multi-Taub-NUT manifolds, showing how they tie in to the bow solutions to Nahm’s equations via the Nahm correspondence. Recently Nakajima and Takayama constructed the Coulomb branch of the moduli space of vacua of a quiver gauge theory, tying them to the same space of bow solutions. One can view our construction as describing the same manifold as the Higgs branch of the mirror gauge theory as described by Cherkis, O’Hara and Saemann. Our construction also yields the monad construction of holomorphic instanton bundles on the multi-Taub-NUT space for any classical compact Lie structure group.

scholarly journals The Volume of the Quiver Vortex Moduli Space

2021 ◽  
Author(s):  
Kazutoshi Ohta ◽  
Norisuke Sakai
Keyword(s):  
Gauge Theory ◽  
Moduli Space ◽  
Riemann Surfaces ◽  
Gauge Theories ◽  
Target Space ◽  
Contour Integral ◽  
Quiver Gauge Theory ◽  
Volume Formula ◽  
Volume Operator ◽  
Space Volume

Abstract We study the moduli space volume of BPS vortices in quiver gauge theories on compact Riemann surfaces. The existence of BPS vortices imposes constraints on the quiver gauge theories. We show that the moduli space volume is given by a vev of a suitable cohomological operator (volume operator) in a supersymmetric quiver gauge theory, where BPS equations of the vortices are embedded. In the supersymmetric gauge theory, the moduli space volume is exactly evaluated as a contour integral by using the localization. Graph theory is useful to construct the supersymmetric quiver gauge theory and to derive the volume formula. The contour integral formula of the volume (generalization of the Jeffrey-Kirwan residue formula) leads to the Bradlow bounds (upper bounds on the vorticity by the area of the Riemann surface divided by the intrinsic size of the vortex). We give some examples of various quiver gauge theories and discuss properties of the moduli space volume in these theories. Our formula are applied to the volume of the vortex moduli space in the gauged non-linear sigma model with CPN target space, which is obtained by a strong coupling limit of a parent quiver gauge theory. We also discuss a non-Abelian generalization of the quiver gauge theory and “Abelianization” of the volume formula.

scholarly journals The ABCDEFG of little strings

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Nathan Haouzi ◽  
Can Kozçaz
Keyword(s):  
Gauge Theory ◽  
Partition Function ◽  
Coulomb Gas ◽  
Conformal Block ◽  
Coulomb Branch ◽  
Quiver Gauge Theory ◽  
Codimension Two ◽  
Type Iib String Theory ◽  
Unified Description ◽  
Formula Type

Abstract Starting from type IIB string theory on an ADE singularity, the (2, 0) little string arises when one takes the string coupling gs to 0. In this setup, we give a unified description of the codimension-two defects of the little string, labeled by a simple Lie algebra $$ \mathfrak{g} $$ g . Geometrically, these are D5 branes wrapping 2-cycles of the singularity, subject to a certain folding operation when the algebra is non simply-laced. Equivalently, the defects are specified by a certain set of weights of $$ {}^L\mathfrak{g} $$ L g , the Langlands dual of $$ \mathfrak{g} $$ g . As a first application, we show that the instanton partition function of the $$ \mathfrak{g} $$ g -type quiver gauge theory on the defect is equal to a 3-point conformal block of the $$ \mathfrak{g} $$ g -type deformed Toda theory in the Coulomb gas formalism. As a second application, we argue that in the (2, 0) CFT limit, the Coulomb branch of the defects flows to a nilpotent orbit of $$ \mathfrak{g} $$ g .

scholarly journals Coulomb Branch of a Multiloop Quiver Gauge Theory

2019 ◽  
Vol 53 (4) ◽  
pp. 241-249
Author(s):  
E. A. Goncharov ◽  
M. V. Finkelberg
Keyword(s):  
Gauge Theory ◽  
Coulomb Branch ◽  
Quiver Gauge Theory

scholarly journals Factorised 3d $$ \mathcal{N} $$ = 4 orthosymplectic quivers

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Mohammad Akhond ◽  
Federico Carta ◽  
Siddharth Dwivedi ◽  
Hirotaka Hayashi ◽  
Sung-Soo Kim ◽  
...  
Keyword(s):  
Moduli Space ◽  
Gauge Theories ◽  
Hilbert Series ◽  
Point Of View ◽  
Coulomb Branch ◽  
Dual Pairs ◽  
Superconformal Field Theories ◽  
Quiver Gauge Theory ◽  
Highest Weight ◽  
Exceptional Sequences

Abstract We study the moduli space of 3d $$ \mathcal{N} $$ N = 4 quiver gauge theories with unitary, orthogonal and symplectic gauge nodes, that fall into exceptional sequences. We find that both the Higgs and Coulomb branches of the moduli space factorise into decoupled sectors. Each decoupled sector is described by a single quiver gauge theory with only unitary gauge nodes. The orthosymplectic quivers serve as magnetic quivers for 5d $$ \mathcal{N} $$ N = 1 superconformal field theories which can be engineered in type IIB string theories both with and without an O5 plane. We use this point of view to postulate the dual pairs of unitary and orthosymplectic quivers by deriving them as magnetic quivers of the 5d theory. We use this correspondence to conjecture exact highest weight generating functions for the Coulomb branch Hilbert series of the orthosymplectic quivers, and provide tests of these results by directly computing the Hilbert series for the orthosymplectic quivers in a series expansion.

scholarly journals An $$ \mathcal{N} $$ = 1 Lagrangian for an $$ \mathcal{N} $$ = 3 SCFT

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Gabi Zafrir
Keyword(s):  
Gauge Theory ◽  
Chiral Field ◽  
Coulomb Branch ◽  
Superconformal Symmetry ◽  
Marginal Deformations ◽  
Marginal Deformation

Abstract We propose that a certain 4d$$ \mathcal{N} $$ N = 1 SU(2) × SU(2) gauge theory flows in the IR to an $$ \mathcal{N} $$ N = 3 SCFT plus a single free chiral field. The specific $$ \mathcal{N} $$ N = 3 SCFT has rank 1 and a dimension three Coulomb branch operator. The flow is generically expected to land at the $$ \mathcal{N} $$ N = 3 SCFT deformed by the marginal deformation associated with said Coulomb branch operator. We also present a discussion about the properties expected of various RG invariant quantities from $$ \mathcal{N} $$ N = 3 superconformal symmetry, and use these to test our proposal. Finally, we discuss a generalization to another $$ \mathcal{N} $$ N = 1 model that we propose is related to a certain rank 3 $$ \mathcal{N} $$ N = 3 SCFT through the turning of certain marginal deformations.

scholarly journals Instanton bundles on two Fano threefolds of index 1

2020 ◽  
Vol 32 (5) ◽  
pp. 1315-1336
Author(s):  
Gianfranco Casnati ◽  
Ozhan Genc
Keyword(s):  
Irreducible Component ◽  
Moduli Space ◽  
Blow Up ◽  
Explicit Construction ◽  
Fano Threefolds ◽  
Instanton Bundles

AbstractWe deal with instanton bundles on the product {\mathbb{P}^{1}\times\mathbb{P}^{2}} and the blow up of {\mathbb{P}^{3}} along a line. We give an explicit construction leading to instanton bundles. Moreover, we also show that they correspond to smooth points of a unique irreducible component of their moduli space.

scholarly journals DISCRETE AND CONTINUUM APPROACHES TO THREE-DIMENSIONAL QUANTUM GRAVITY

1991 ◽  
Vol 06 (39) ◽  
pp. 3591-3600 ◽  
Author(s):  
HIROSI OOGURI ◽  
NAOKI SASAKURA
Keyword(s):  
Gauge Theory ◽  
Moduli Space ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Analogue Model ◽  
Gauge Invariant ◽  
Invariant Functions ◽  
Dimensional Lattice ◽  
Chern Simons ◽  
Dimensional Surface

It is shown that, in the three-dimensional lattice gravity defined by Ponzano and Regge, the space of physical states is isomorphic to the space of gauge-invariant functions on the moduli space of flat SU(2) connections over a two-dimensional surface, which gives physical states in the ISO(3) Chern–Simons gauge theory. To prove this, we employ the q-analogue of this model defined by Turaev and Viro as a regularization to sum over states. A recent work by Turaev suggests that the q-analogue model itself may be related to an Euclidean gravity with a cosmological constant proportional to 1/k2, where q=e2πi/(k+2).

scholarly journals Mocking the u-plane integral

2021 ◽  
Vol 8 (3) ◽  
Author(s):  
Georgios Korpas ◽  
Jan Manschot ◽  
Gregory W. Moore ◽  
Iurii Nidaiev
Keyword(s):  
Asymptotic Behavior ◽  
Gauge Theory ◽  
Entire Function ◽  
Gauge Group ◽  
Strong Coupling ◽  
Modular Forms ◽  
Correlation Functions ◽  
Coulomb Branch ◽  
Mock Modular Forms ◽  
Donaldson Invariants

AbstractThe u-plane integral is the contribution of the Coulomb branch to correlation functions of $${\mathcal {N}}=2$$ N = 2 gauge theory on a compact four-manifold. We consider the u-plane integral for correlators of point and surface observables of topologically twisted theories with gauge group $$\mathrm{SU}(2)$$ SU ( 2 ) , for an arbitrary four-manifold with $$(b_1,b_2^+)=(0,1)$$ ( b 1 , b 2 + ) = ( 0 , 1 ) . The u-plane contribution equals the full correlator in the absence of Seiberg–Witten contributions at strong coupling, and coincides with the mathematically defined Donaldson invariants in such cases. We demonstrate that the u-plane correlators are efficiently determined using mock modular forms for point observables, and Appell–Lerch sums for surface observables. We use these results to discuss the asymptotic behavior of correlators as function of the number of observables. Our findings suggest that the vev of exponentiated point and surface observables is an entire function of the fugacities.

scholarly journals Recursive relations for a quiver gauge theory

2006 ◽  
Vol 2006 (10) ◽  
pp. 026-026 ◽  
Author(s):  
Jaemo Park ◽  
Woojoo Sim
Keyword(s):  
Gauge Theory ◽  
Quiver Gauge Theory ◽  
Recursive Relations

Moduli Space, of supersymmetric gauge theory

2004 ◽  
pp. 244-244
Author(s):  
David Berman ◽  
Hugo Garcia-Compean ◽  
Paulius Miškinis ◽  
Miao Li ◽  
Daniele Oriti ◽  
...  
Keyword(s):  
Supersymmetric Gauge Theory ◽  
Gauge Theory ◽  
Moduli Space ◽  
Supersymmetric Gauge
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