We study non-planar corrections in two special $\mathcal N=2$ superconformal $SU(N)$ gauge theories that are planar-equivalent to $\mathcal N=4$ SYM theory: two-nodes quiver model with equal ...couplings and $\mathcal N=2$ vector multiplet coupled to two hypermultiplets in rank-2 symmetric and antisymmetric representations. We focus on two observables in these theories that admit representation in terms of localization matrix model: free energy on 4-sphere and the expectation value of half-BPS circular Wilson loop. We extend the methods developed in arXiv:2207.11475 to derive a systematical expansion of non-planar corrections to these observables at strong 't Hooft coupling constant $\lambda$. We show that the leading non planar corrections are given by a power series in $\lambda^{3/2}/N^2$ with rational coefficients. Sending $N$ and the coupling constant $\lambda$ to infinity with $\lambda^{3/2}/N^2$ kept fixed corresponds to the familiar double scaling limit in matrix models. We find that in this limit the observables in the two models are related in a remarkably simple way: the free energies differ by the factor of $2$, whereas the Wilson loop expectation values coincide. Surprisingly, these relations hold only at strong coupling, they are not valid in the weak coupling regime. We also discuss a dual string theory interpretation of the leading corrections to the free energy in the double scaling limit suggesting their relation to curvature corrections in type IIB string effective action.
We consider the Z polarization asymmetry AZ=(σ(ZR)−σ(ZL))/(σ(ZR)+σ(ZL)) in the process of associated bZ production at the LHC. We show that in the Standard Model (SM) this quantity is essentially ...given by its Born approximation, remaining almost unaffected by QCD scales and parton distribution functions variations as well as by electroweak corrections. The theoretical quantity that appears in AZ is the same that provides the LEP1 Z→bb¯ forward–backward asymmetry, the only measured observable still in some contradiction with the SM prediction. In this sense, AZ would provide the possibility of an independent verification of the possible SM discrepancy, which could reach, if consistency with LEP1 measurements is imposed, values of the relative ten percent size.
A
bstract
Extending earlier work, we find the two-loop term in the beta-function for the scalar coupling
ζ
in a generalized Wilson loop operator of the
$$ \mathcal{N} $$
N
= 4 SYM theory, working in ...the planar weak-coupling expansion. The beta-function for
ζ
has fixed points at
ζ
= ±1 and
ζ
= 0, corresponding respectively to the supersymmetric Wilson-Maldacena loop and to the standard Wilson loop without scalar coupling. As a consequence of our result for the beta-function, we obtain a prediction for the two-loop term in the anomalous dimension of the scalar field inserted on the standard Wilson loop. We also find a subset of higher-loop contributions (with highest powers of
ζ
at each order in ‘t Hooft coupling
λ
) coming from the scalar ladder graphs determining the corresponding terms in the five-loop beta-function. We discuss the related structure of the circular Wilson loop expectation value commenting, in particular, on consistency with a 1d defect version of the F-theorem. We also compute (to two loops in the planar ladder model approximation) the two-point correlators of scalars inserted on the Wilson line.
We consider strong 't Hooft coupling expansion in special four-dimensional $\mathcal N=2$ superconformal models that are planar-equivalent to $\mathcal N=4$ super Yang-Mills theory. Various ...observables in these models that admit localization matrix model representation can be expressed at large $N$ in terms of a Fredholm determinant of a Bessel operator. The latter previously appeared in the study of level spacing distributions in matrix models and, more recently, in four-point correlation functions of infinitely heavy half-BPS operators in planar $\mathcal N=4$ SYM. We use this relation and a suitably generalized Szego-Akhiezer-Kac formula to derive the strong 't Hooft coupling expansion of the leading corrections to free energy, half-BPS circular Wilson loop, and certain correlators of chiral primaries operators in the $\mathcal N=2$ models. This substantially generalizes partial results in the literature and represents a challenge for dual string theory calculations in AdS/CFT context. We also demonstrate that the resulting strong-coupling expansions suffer from Borel singularities and require adding non-perturbative, exponentially suppressed corrections. As a byproduct of our analysis, we determine the non-perturbative correction to the above mentioned four-point correlator in planar $\mathcal N=4$ SYM.
Many extensions of the Standard Model involve two Higgs doublet fields to break the electroweak symmetry, leading to the existence of three neutral and two charged Higgs particles. In particular, ...this is the case of the Minimal Supersymmetric extension of the Standard Model, the MSSM. A very important parameter is tanβ defined as the ratio of the vacuum expectation value of the two Higgs doublets. In this Letter we focus on the left–right asymmetry in the production of polarised top quarks in association with charged Higgs bosons at the LHC. This quantity allows for a theoretically clean determination of tanβ. In the MSSM, the asymmetry remains sensitive to the strong and electroweak radiative corrections and, thus, to the superparticle spectrum. Some possible implications of these results are discussed.
N = 2 Conformal SYM theories at large N Beccaria, M.; Billò, M.; Galvagno, F. ...
The journal of high energy physics,
09/2020, Letnik:
2020, Številka:
9
Journal Article
Recenzirano
Odprti dostop
A
bstract
We consider a class of
N
= 2 conformal SU(
N
) SYM theories in four dimensions with matter in the fundamental, two-index symmetric and anti-symmetric representations, and study the ...corresponding matrix model provided by localization on a sphere
S
4
, which also encodes information on flat-space observables involving chiral operators and circular BPS Wilson loops. We review and improve known techniques for studying the matrix model in the large-
N
limit, deriving explicit expressions in perturbation theory for these observables. We exploit both recursive methods in the so-called full Lie algebra approach and the more standard Cartan sub-algebra approach based on the eigenvalue distribution. The sub-class of conformal theories for which the number of fundamental hypermultiplets does not scale with
N
differs in the planar limit from the
N
= 4 SYM theory only in observables involving chiral operators of odd dimension. In this case we are able to derive compact expressions which allow to push the small ’t Hooft coupling expansion to very high orders. We argue that the perturbative series have a finite radius of convergence and extrapolate them numerically to intermediate couplings. This is preliminary to an analytic investigation of the strong coupling behavior, which would be very interesting given that for such theories holographic duals have been proposed.
The inhibitive action of MAOS (metacryloxypropylmethoxysilane) used for silanising pre-treatment on aluminium corrosion in NaCl aqueous 3.5% solutions has been examined.
Free corrosion and ...electrochemical tests (potentiodynamic polarisation and electrochemical impedance) were performed to characterise the resistance of pre-treated specimens against general and localised corrosion.
The surface of the specimens was examined by XPS, FT/IR and optical microscopy before and after immersion in NaCl solution.
It was found that silanising inhibits general and localised corrosion of aluminium because of the formation of an Al–siloxane polymeric film, the inhibitive action of which increases with increasing immersion time due to the synergistic effect of aluminium oxides precipitated as corrosion products on aluminium surfaces.
Abstract We consider the refined Schur superconformal index of 4d N $$ \mathcal{N} $$ = 4 U(N) SYM and the first term of its giant-graviton expansion, first predicted in arXiv:2001.11667 using ...indirect superconformal algebra considerations and analytic continuation of fugacities. This correction is the leading non-perturbative correction to the index at large N and we reproduce it from the semiclassical partition function of quantum D3 brane wrapped on S 1 × S 3 in a twisted modification of the AdS 5 × S 5 string background, depending on the index R-symmetry fugacity. Our calculation does not exploit directly supersymmetry. It is based on the determination of the partition function of the various bosonic and fermionic fluctuations on the wrapped brane whose action is conformal with specific constant holonomies along thermal cycle. We show how those partition functions may be obtained by adapting the operator counting method of Cardy to the twisted background.
A
bstract
We study non-planar corrections in two special
$$ \mathcal{N} $$
N
= 2 superconformal SU(
N
) gauge theories that are planar-equivalent to
$$ \mathcal{N} $$
N
= 4 SYM theory: two-nodes ...quiver model with equal couplings and
$$ \mathcal{N} $$
N
= 2 vector multiplet coupled to two hypermultiplets in rank-2 symmetric and antisymmetric representations. We focus on two observables in these theories that admit representation in terms of localization matrix model: free energy on 4-sphere and the expectation value of half-BPS circular Wilson loop. We extend the methods developed in arXiv:2207.11475 to derive a systematical expansion of non-planar corrections to these observables at strong ’t Hooft coupling constant
λ
. We show that the leading non- planar corrections are given by a power series in
λ
3
/
2
/N
2
with rational coefficients. Sending
N
and the coupling constant
λ
to infinity with
λ
3
/
2
/N
2
kept fixed corresponds to the familiar double scaling limit in matrix models. We find that in this limit the observables in the two models are related in a remarkably simple way: the free energies differ by the factor of 2, whereas the Wilson loop expectation values coincide. Surprisingly, these relations hold only at strong coupling, they are not valid in the weak coupling regime. We also discuss a dual string theory interpretation of the leading corrections to the free energy in the double scaling limit suggesting their relation to curvature corrections in type IIB string effective action.
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