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 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 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 Holographic RG flows and universal structures on the Coulomb branch of supersymmetric large- gauge theory

2003 ◽  
Vol 2003 (07) ◽  
pp. 039-039 ◽  
Author(s):  
James E Carlisle ◽  
Clifford V Johnson
Keyword(s):  
Gauge Theory ◽  
Coulomb Branch

scholarly journals Integrating over the Coulomb branch in N = 2 gauge theory

1998 ◽  
Vol 68 (1-3) ◽  
pp. 336-347 ◽  
Author(s):  
Marcos Marino ◽  
Gregory Moore
Keyword(s):  
Gauge Theory ◽  
Coulomb Branch

scholarly journals Five-dimensional SCFTs and gauge theory phases: an M-theory/type IIA perspective

2019 ◽  
Vol 6 (5) ◽  
Author(s):  
Cyril Closset ◽  
Michele Del Zotto ◽  
Vivek Saxena
Keyword(s):  
Field Theory ◽  
Gauge Theory ◽  
Gauge Theories ◽  
Low Energy ◽  
Field Theories ◽  
Isolated Singularity ◽  
Coulomb Branch ◽  
Superconformal Field Theories ◽  
Ale Space ◽  
M Theory

We revisit the correspondence between Calabi-Yau (CY) threefold isolated singularities \mathbf{X}𝐗 and five-dimensional superconformal field theories (SCFTs), which arise at low energy in M-theory on the space-time transverse to \mathbf{X}𝐗. Focussing on the case of toric CY singularities, we analyze the “gauge-theory phases” of the SCFT by exploiting fiberwise M-theory/type IIA duality. In this setup, the low-energy gauge group simply arises on stacks of coincident D6-branes wrapping 2-cycles in some ALE space of type A_{M-1}AM−1 fibered over a real line, and the map between the Kähler parameters of \mathbf{X}𝐗 and the Coulomb branch parameters of the field theory (masses and VEVs) can be read off systematically. Different type IIA “reductions” give rise to different gauge theory phases, whose existence depends on the particular (partial) resolutions of the isolated singularity \mathbf{X}𝐗. We also comment on the case of non-isolated toric singularities. Incidentally, we propose a slightly modified expression for the Coulomb-branch prepotential of 5d \mathcal{N}=1𝒩=1 gauge theories.

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 Holographic Coulomb branch solitons, quasinormal modes, and black holes

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
S. Prem Kumar ◽  
Andy O’Bannon ◽  
Anton Pribytok ◽  
Ronnie Rodgers
Keyword(s):  
Black Holes ◽  
Gauge Theory ◽  
Gauge Symmetry ◽  
Quasinormal Modes ◽  
Coulomb Branch ◽  
Asymptotically Flat ◽  
Yang Mills ◽  
Hooft Coupling ◽  
Qualitative And Quantitative ◽  
Extremal Black Holes

Abstract Four-dimensional $$ \mathcal{N} $$ N = 4 supersymmetric Yang-Mills theory, at a point on the Coulomb branch where SU(N) gauge symmetry is spontaneously broken to SU(N − 1) × U(1), admits BPS solitons describing a spherical shell of electric and/or magnetic charges enclosing a region of unbroken gauge symmetry. These solitons have been proposed as gauge theory models for certain features of asymptotically flat extremal black holes. In the ’t Hooft large N limit with large ’t Hooft coupling, these solitons are holographically dual to certain probe D3-branes in the AdS5 × S5 solution of type IIB supergravity. By studying linearised perturbations of these D3-branes, we show that the solitons support quasinormal modes with a spectrum of frequencies sharing both qualitative and quantitative features with asymptotically flat extremal black holes.

scholarly journals The Coulomb branch of gauge theory from rotating branes

1999 ◽  
Vol 1999 (03) ◽  
pp. 003-003 ◽  
Author(s):  
Per Kraus ◽  
Finn Larsen ◽  
Sandip P Trivedi
Keyword(s):  
Gauge Theory ◽  
Coulomb Branch

scholarly journals Revisiting the multi-monopole point of SU(N) $$ \mathcal{N} $$ = 2 gauge theory in four dimensions

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
Eric D’Hoker ◽  
Thomas T. Dumitrescu ◽  
Efrat Gerchkovitz ◽  
Emily Nardoni
Keyword(s):  
Gauge Theory ◽  
Supersymmetry Breaking ◽  
Integrable Systems ◽  
Gauge Theories ◽  
Magnetic Monopoles ◽  
Coulomb Branch ◽  
Four Dimensions ◽  
Broad Agreement ◽  
Exact Agreement ◽  
Soft Supersymmetry Breaking

Abstract Motivated by applications to soft supersymmetry breaking, we revisit the expansion of the Seiberg-Witten solution around the multi-monopole point on the Coulomb branch of pure SU(N) $$ \mathcal{N} $$ N = 2 gauge theory in four dimensions. At this point N − 1 mutually local magnetic monopoles become massless simultaneously, and in a suitable duality frame the gauge couplings logarithmically run to zero. We explicitly calculate the leading threshold corrections to this logarithmic running from the Seiberg-Witten solution by adapting a method previously introduced by D’Hoker and Phong. We compare our computation to existing results in the literature; this includes results specific to SU(2) and SU(3) gauge theories, the large-N results of Douglas and Shenker, as well as results obtained by appealing to integrable systems or topological strings. We find broad agreement, while also clarifying some lingering inconsistencies. Finally, we explicitly extend the results of Douglas and Shenker to finite N , finding exact agreement with our first calculation.

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