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.

scholarly journals FOUR LECTURES ON THE GAUGE/GRAVITY CORRESPONDENCE

2003 ◽  
Vol 18 (31) ◽  
pp. 5647-5711 ◽  
Author(s):  
MATTEO BERTOLINI
Keyword(s):  
Gauge Theory ◽  
Riemann Surfaces ◽  
Gauge Theories ◽  
Open Problems ◽  
Four Dimensions ◽  
General Overview ◽  
Geometric Transitions ◽  
Supersymmetric Gauge ◽  
Gauge Gravity ◽  
M Theory

We review in a pedagogical manner some of the efforts aimed at extending the gauge/gravity correspondence to nonconformal supersymmetric gauge theories in four dimensions. After giving a general overview, we discuss in detail two specific examples: fractional D-branes on orbifolds and D-branes wrapped on supersymmetric cycles of Calabi–Yau spaces. We explore in particular which gauge theory information can be extracted from the corresponding supergravity solutions, and what the remaining open problems are. We also briefly explain the connection between these and other approaches, such as fractional branes on conifolds, branes suspended between branes, M5-branes on Riemann surfaces and M-theory on G2-holonomy manifolds, and discuss the role played by geometric transitions in all that.

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 CONFINEMENT IN GAUGE THEORIES FROM THE CONDENSATION OF WORLD SHEET DEFECTS IN LIOUVILLE STRING

1999 ◽  
Vol 14 (24) ◽  
pp. 3761-3788 ◽  
Author(s):  
JOHN ELLIS ◽  
N. E. MAVROMATOS
Keyword(s):  
Black Holes ◽  
Gauge Theory ◽  
Wilson Loop ◽  
Degrees Of Freedom ◽  
Gauge Theories ◽  
String Tension ◽  
Magnetic Monopoles ◽  
Target Space ◽  
De Sitter ◽  
World Sheet

We present a Liouville-string approach to confinement in four-dimensional gauge theories, which extends previous approaches to include nonconformal theories. We consider Liouville field theory on world sheets whose boundaries are the Wilson loops of gauge theory, which exhibit vortex and spike defects. We show that world sheet vortex condensation occurs when the Wilson loop is embedded in four target–space–time dimensions, and show that this corresponds to the condensation of gauge magnetic monopoles in target–space. We also show that vortex condensation generates an effective string tension corresponding to the confinement of electric degrees of freedom. The tension is independent of the string length in a gauge theory whose electric coupling varies logarithmically with the length scale. The Liouville field is naturally interpreted as an extra target dimension, with an anti-de-Sitter (AdS) structure induced by recoil effects on the gauge monopoles, interpreted as D branes of the effective string theory. Black holes in the bulk AdS space correspond to world sheet defects, so that phases of the bulk gravitational system correspond to the different world sheet phases, and hence to different phases of the four-dimensional gauge theory. Deconfinement is associated with a Berezinskii–Kosterlitz–Thouless transition of vortices on the Wilson-loop world sheet, corresponding in turn to a phase transition of the black holes in the bulk AdS space.

scholarly journals CURRENT ALGEBRA AND SUPERSYMMETRY

1986 ◽  
Vol 01 (03) ◽  
pp. 499-544 ◽  
Author(s):  
G.M. SHORE ◽  
G. VENEZIANO
Keyword(s):  
Supersymmetry Breaking ◽  
Current Algebra ◽  
Gauge Theories ◽  
Critical Assessment ◽  
Ward Identities ◽  
Yang Mills ◽  
Effective Lagrangian ◽  
Soft Supersymmetry Breaking ◽  
Supersymmetric Gauge ◽  
Chiral Superfield

The implications of supersymmetry and chiral Ward identities in supersymmetric gauge theories are explored using current algebra methods, and a critical assessment is made of the relative merits of the current algebra and effective Lagrangian approaches. Using the Ward identities directly, simple derivations are given of several important properties of the condensates in supersymmetric QCD, and of the generalized Dashen formulae. The corrections to these results in the presence of explicit, soft supersymmetry breaking are calculated. A concise formula is presented for the mass splittings within pseudo Goldstone multiplets induced by soft supersymmetry breaking terms. It is shown that if this supersymmetry breaking is the θ=0 component of a chiral superfield, the supertrace of the pseudo Goldstone masses vanishes. Using current algebra reduction formulae, the pseudo Goldstone masses are calculated in supersymmetric Yang-Mills theory, and supersymmetric QCD for NF<NC and NF=NC. Some differences are found between the current algebra and effective Lagrangian predictions, and their possible origins are discussed.

scholarly journals The non-SUSY baryonic branch: soft supersymmetry breaking of $ \mathcal{N} = 1 $ gauge theories

2012 ◽  
Vol 2012 (5) ◽  
Author(s):  
Stephen Bennett ◽  
Elena Caceres ◽  
Carlos Núñez ◽  
Daniel Schofield ◽  
Steve Young
Keyword(s):  
Supersymmetry Breaking ◽  
Gauge Theories ◽  
Soft Supersymmetry Breaking

LONG DISTANCE DYNAMICS AND CONFINEMENT VIA RG DECIMATIONS

2009 ◽  
Vol 24 (34) ◽  
pp. 2717-2730 ◽  
Author(s):  
E. T. TOMBOULIS
Keyword(s):  
Fixed Point ◽  
Renormalization Group ◽  
Gauge Theory ◽  
Gauge Theories ◽  
Upper And Lower Bounds ◽  
Free Energies ◽  
Long Distance ◽  
Strongly Coupled ◽  
Four Dimensions ◽  
Lattice Regularization

We review a recently developed framework employing computable Renormalization Group (RG) decimations for gauge theories in the lattice regularization. They provide upper and lower bounds at every scale for free energies and some order parameters. By interpolating between these bounds representations of the exact quantities are obtained at progressively longer scales (coarser lattices). In the case of the SU(2) gauge theory in four dimensions RG flow to the confining strongly coupled regime is obtained for any initial coupling; whereas for the U(1) theory a fixed point is reached for small initial coupling.

scholarly journals Scattering amplitudes and the double copy in topologically massive theories

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Nathan Moynihan
Keyword(s):  
Gauge Theory ◽  
Scattering Amplitudes ◽  
Gauge Theories ◽  
Three Dimensional ◽  
Landau Gauge ◽  
Massive Gravity ◽  
Gauge Bosons ◽  
Four Dimensions ◽  
Recent Developments ◽  
Double Copy

Abstract Using the principles of the modern scattering amplitudes programme, we develop a formalism for constructing the amplitudes of three-dimensional topologically massive gauge theories and gravity. Inspired by recent developments in four dimensions, we construct the three-dimensional equivalent of x-variables, first defined in [1], for conserved matter currents coupled to topologically massive gauge bosons or gravitons. Using these, we bootstrap various matter-coupled gauge-theory and gravitational scattering amplitudes, and conjecture that topologically massive gauge theory and topologically massive gravity are related by the double copy. To motivate this idea further, we show explicitly that the Landau gauge propagator on the gauge theory side double copies to the de Donder gauge propagator on the gravity side.

scholarly journals New 2d $$ \mathcal{N} $$ = (0, 2) dualities from four dimensions

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Matteo Sacchi
Keyword(s):  
Gauge Theory ◽  
Gauge Theories ◽  
Negative Integer ◽  
Arbitrary Length ◽  
Four Dimensions ◽  
Elliptic Genera ◽  
Infra Red

Abstract We propose some new infra-red dualities for 2d$$ \mathcal{N} $$ N = (0, 2) theories. The first one relates a USp(2N) gauge theory with one antisymmetric chiral, four fundamental chirals and N Fermi singlets to a Landau-Ginzburg model of N Fermi and 6N chiral fields with cubic interactions. The second one relates SU(2) linear quiver gauge theories of arbitrary length N − 1 with the addition of N Fermi singlets for any non-negative integer N. They can be understood as a generalization of the duality between an SU(2) gauge theory with four fundamental chirals and a Landau-Ginzburg model of one Fermi and six chirals with a cubic interaction. We derive these dualities from already known 4d$$ \mathcal{N} $$ N = 1 dualities by compactifications on $$ {\mathbbm{S}}^2 $$ S 2 with suitable topological twists and we further test them by matching anomalies and elliptic genera. We also show how to derive them by iterative applications of some more fundamental dualities, in analogy with similar derivations for parent dualities in three and four dimensions.

scholarly journals ASPECTS OF INTEGRABILITY IN $\mathcal{N} = 4$ SYM

2007 ◽  
Vol 22 (34) ◽  
pp. 2549-2563 ◽  
Author(s):  
ABHISHEK AGARWAL
Keyword(s):  
Gauge Theory ◽  
Integrable Systems ◽  
Closed String ◽  
Quantum Spin ◽  
Spin Chains ◽  
Quantum Spin Chains ◽  
Four Dimensions ◽  
Yang Mills ◽  
Open Strings

Various recently developed connections between supersymmetric Yang–Mills theories in four dimensions and two-dimensional integrable systems serve as crucial ingredients in improving our understanding of the AdS/CFT correspondence. In this review, we highlight some connections between superconformal four-dimensional Yang–Mills theory and various integrable systems. In particular, we focus on the role of Yangian symmetries in studying the gauge theory dual of closed string excitations. We also briefly review how the gauge theory connects to Calogero models and open quantum spin chains through the study of the gauge theory duals of D3 branes and open strings ending on them. This invited review is based on a seminar given at the Institute of Advanced Study, Princeton.

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