scholarly journals Fermi-gas correlators of ADHM theory and triality symmetry

2022 ◽  
Vol 12 (1) ◽  
Author(s):  
Yasuyuki Hatsuda ◽  
Tadashi Okazaki
Keyword(s):  
Gauge Group ◽  
Correlation Functions ◽  
Canonical Correlation ◽  
Fermi Gas ◽  
Coulomb Branch ◽  
M Theory ◽  
Grand Canonical

We analytically study the Fermi-gas formulation of sphere correlation functions of the Coulomb branch operators for 3d \mathcal{N}=4𝒩=4 ADHM theory with a gauge group U(N)U(N), an adjoint hypermultiplet and ll hypermultiplets which can describe a stack of NN M2-branes at A_{l-1}Al−1 singularities. We find that the leading coefficients of the perturbative grand canonical correlation functions are invariant under a hidden triality symmetry conjectured from the twisted M-theory. The triality symmetry also helps us to fix the next-to-leading corrections analytically.

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 Superconformal duality-invariant models and $$ \mathcal{N} $$ = 4 SYM effective action

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
Sergei M. Kuzenko
Keyword(s):  
Gauge Group ◽  
Nonlinear Theory ◽  
Effective Action ◽  
Low Energy ◽  
Vector Multiplet ◽  
Coulomb Branch ◽  
Conformal Supergravity ◽  
Yang Mills ◽  
Planar Part ◽  
Invariant Coupling

Abstract We present $$ \mathcal{N} $$ N = 2 superconformal U(1) duality-invariant models for an Abelian vector multiplet coupled to conformal supergravity. In a Minkowski background, such a nonlinear theory is expected to describe (the planar part of) the low-energy effective action for the $$ \mathcal{N} $$ N = 4 SU(N) super-Yang-Mills (SYM) theory on its Coulomb branch where (i) the gauge group SU(N) is spontaneously broken to SU(N − 1) × U(1); and (ii) the dynamics is captured by a single $$ \mathcal{N} $$ N = 2 vector multiplet associated with the U(1) factor of the unbroken group. Additionally, a local U(1) duality-invariant action generating the $$ \mathcal{N} $$ N = 2 super-Weyl anomaly is proposed. By providing a new derivation of the recently constructed U(1) duality-invariant $$ \mathcal{N} $$ N = 1 superconformal electrodynamics, we introduce its SL(2, ℝ) duality-invariant coupling to the dilaton-axion multiplet.

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.

STUDY OF ISOSCALING PHENOMENA FOR PROJECTILE-LIKE FRAGMENTS

2006 ◽  
Vol 15 (08) ◽  
pp. 1803-1812
Author(s):  
Q. M. SU ◽  
D. Q. FANG ◽  
Y. G. MA ◽  
C. ZHONG ◽  
C. W. MA ◽  
...  
Keyword(s):  
Experimental Data ◽  
Equation Of State ◽  
Linear Dependence ◽  
Fermi Gas ◽  
Heavy Ion ◽  
Projectile Fragmentation ◽  
Reaction Systems ◽  
Nuclear Equation Of State ◽  
Ion Collisions ◽  
Grand Canonical

In the framework of a modified statistical abrasion-ablation (SAA) model, the isospin effect and isoscaling behavior in projectile fragmentation have been systematically investigated. The normalized peak differences and reduced isoscaling parameters are found to decrease with (Z proj -Z)/Z proj and have no significant dependence on the size of reaction systems. The linear dependence of α and |β| on [Formula: see text] or [Formula: see text] for projectile-like fragments is demonstrated, which is obtained for light fragments from multifragmentation in the grand-canonical limit. Assuming a Fermi-gas behavior, the excitation energy dependence of the symmetry energy coefficients are tentatively extracted from α and β which looks consistent with the experimental data. It is pointed out that the reduced isoscaling parameters can be used as an observable to study the excitation extent of system and asymmetric nuclear equation of state in heavy ion collisions.

scholarly journals Conformal blocks from celestial gluon amplitudes

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Wei Fan ◽  
Angelos Fotopoulos ◽  
Stephan Stieberger ◽  
Tomasz R. Taylor ◽  
Bin Zhu
Keyword(s):  
Gauge Group ◽  
Correlation Functions ◽  
Delta Function ◽  
Adjoint Representation ◽  
Conformal Block ◽  
Group Representations ◽  
Conformal Blocks ◽  
Four Dimensions ◽  
Point Correlation ◽  
Complex Spin

Abstract In celestial conformal field theory, gluons are represented by primary fields with dimensions ∆ = 1 + iλ, λ ∈ ℝ and spin J = ±1, in the adjoint representation of the gauge group. All two- and three-point correlation functions of these fields are zero as a consequence of four-dimensional kinematic constraints. Four-point correlation functions contain delta-function singularities enforcing planarity of four-particle scattering events. We relax these constraints by taking a shadow transform of one field and perform conformal block decomposition of the corresponding correlators. We compute the conformal block coefficients. When decomposed in channels that are “compatible” in two and four dimensions, such four-point correlators contain conformal blocks of primary fields with dimensions ∆ = 2 + M + iλ, where M ≥ 0 is an integer, with integer spin J = −M, −M + 2, …, M − 2, M. They appear in all gauge group representations obtained from a tensor product of two adjoint representations. When decomposed in incompatible channels, they also contain primary fields with continuous complex spin, but with positive integer dimensions.

scholarly journals Twisted circle compactifications of 6d SCFTs

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Lakshya Bhardwaj ◽  
Patrick Jefferson ◽  
Hee-Cheol Kim ◽  
Houri-Christina Tarazi ◽  
Cumrun Vafa
Keyword(s):  
Field Theories ◽  
Geometric Description ◽  
Coulomb Branch ◽  
Superconformal Field Theories ◽  
Physical Data ◽  
Algebraic Description ◽  
Genus One ◽  
M Theory ◽  
Kaluza Klein

Abstract We study 6d superconformal field theories (SCFTs) compactified on a circle with arbitrary twists. The theories obtained after compactification, often referred to as 5d Kaluza-Klein (KK) theories, can be viewed as starting points for RG flows to 5d SCFTs. According to a conjecture, all 5d SCFTs can be obtained in this fashion. We compute the Coulomb branch prepotential for all 5d KK theories obtainable in this manner and associate to these theories a smooth local genus one fibered Calabi-Yau threefold in which is encoded information about all possible RG flows to 5d SCFTs. These Calabi-Yau threefolds provide hitherto unknown M-theory duals of F-theory configurations compactified on a circle with twists. For certain exceptional KK theories that do not admit a standard geometric description we propose an algebraic description that appears to retain the properties of the local Calabi-Yau threefolds necessary to determine RG flows to 5d SCFTs, along with other relevant physical data.

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