Running Gauge Coupling Research Articles

A note on the dual of [formula omitted] super-Yang–Mills theory

We refine the dictionary of the gauge/gravity correspondence realizing N=1 super-Yang–Mills by means of D5-branes wrapped on a resolved Calabi–Yau space. This is done by fixing an ambiguity on the correct interpretation of the holographic dual of the running gauge coupling and amounts to identify a specific 2-cycle in the dual ten-dimensional supergravity background. In doing so, we also discuss the role played in this context by gauge transformations in the relevant seven-dimensional gauged supergravity. While all nice properties of the duality are maintained, this modification of the dictionary has some interesting physical consequences and solves a puzzle recently raised in the literature. In this refined framework, it is also straightforward to see how the correspondence naturally realizes a geometric transition.

Running of Gauge Couplings inAdS5via Deconstruction

Running of gauge couplings on a slice of AdS5 is examined using the deconstruction set-up. Logarithmic running instead of (linear) power law is justified when the cutoff is lower than the curvature scale. Most of interesting features in warped gauge theory including the localization of Kaluza-Klein modes, the widening of higher Kaluza-Klein spectrum spacing are well captured within the framework of the deconstruction.

Field Theory Operator Encoding in Script N = 2 Geometries

We investigate supergravity solutions describing D5 branes wrapped on a two cycle which are dual to N=2 super Yang Mills theory. Brane probing these solutions allows the moduli space of the field theory to be identified. There are a unique set of coordinates in which the field theory on the probe takes an N=2 form and in these coordinates the running coupling of the gauge theory may be identified. We show that the geometry, when restricted to the moduli space, takes a very simple form involving only two functions. One is the running gauge coupling whilst the other parametrizes the scalar operators of the field theory. The D5 brane distributions, for the full set of solutions in the literature,can be determined by assuming the field theory's form for the running coupling as a function of scalar vevs. We show that the resulting distributions also correctly reproduce the scalar operators parametrized elsewhere providing the first non-trivial consistency check on the duality.

A minimal S1/( Z2× Z2′) orbifold GUT

We investigate supersymmetric SU(5) grand unified theories (GUTs) realized in 5 space time dimensions and broken down to the MSSM by SU(5)-violating boundary conditions on a S 1/( Z 2× Z 2′) orbifold with two 3-branes. The doublet-triplet splitting problem is entirely avoided by locating the MSSM Higgs doublets on the brane on which SU(5) is not a good symmetry. An extremely simple model is then described in which the MSSM matter is also located on this SU(5)-violating brane. Although this model does not unify the MSSM matter within SU(5) multiplets, it explains gauge coupling unification. A second model with MSSM matter in the SU(5)-symmetric bulk preserves both the SU(5) explanation of fermion quantum numbers as well as gauge-coupling unification. Both models naturally avoid problematic SU(5) predictions for the Yukawa couplings of the first two generations and are consistent with proton decay constraints. We analyse the running of gauge couplings above the compactification scale in terms of a 5d effective action and derive the implications for the values of compactification scale, unification scale and of the scale at which the bulk gauge theory becomes strongly coupled.

QUANTUM DILATONIC GRAVITY IN d=2,4 AND 5 DIMENSIONS

We review (mainly) quantum effects in the theories where the gravity sector is described by metric and dilaton. The one-loop effective action for dilatonic gravity in two and four dimensions is evaluated. Renormalization group equations are constructed. The conformal anomaly and induced effective action for 2d and 4d dilaton coupled theories are found. It is applied to the study of quantum aspects of black hole thermodynamics, like calculation of Hawking radiation and quantum corrections to black hole parameters and investigation of quantum instability for such objects with multiple horizons. The use of the above effective action in the construction of nonsingular cosmological models in Einstein or Brans–Dicke (super)gravity and investigation of induced wormholes in supersymmetric Yang–Mills theory are given.5d dilatonic gravity (bosonic sector of compactified IIB supergravity) is discussed in connection with bulk/boundary (or AdS/CFT) correspondence. Running gauge coupling and quark–antiquark potential for boundary gauge theory at zero or nonzero temperature are calculated from d=5 dilatonic anti-de Sitter-like background solution which represents anti-de Sitter black hole for periodic time.

Curvature dependence of running gauge coupling and confinement in AdS-CFT correspondence

We construct IIB supergravity (viewed as dilatonic gravity) background with non-trivial dilaton and with curved four-dimensional space. Such a background may describe another vacuum of maximally supersymmetric Yang-Mills theory or strong coupling regime of (non)-supersymmetric gauge theory with (power-like) running gauge coupling which depends on curvature. Curvature dependent quark-antiquark potential is calculated where the geometry type of hyperbolic (or de Sitter universe) shows (or not) the tendency of the confinement. Generalization of IIB supergravity background with non-constant axion is presented. Quark-antiquark potential being again curvature-dependent has a possibility to produce the standard area law for large separations.

Running gauge coupling and quark-antiquark potential in non-SUSY gauge theory at finite temperature from type IIB supergravity-CFT correspondence

We discuss the non-constant dilaton deformed ${\rm AdS}_5\times{\rm S}_5$ solutions of IIB supergravity where AdS sector is described by black hole. The investigation of running gauge coupling (exponent of dilaton) of non-SUSY gauge theory at finite temperature is presented for different regimes (high or low T, large radius expansion). Running gauge coupling shows power-like behavior on temperature with stable fixed point. The quark-antiquark potential at finite T is found and possibility of confinement is established. It is shown that non-constant dilaton affects the potential, sometimes reversing its behavior if we compare it with the constant dilaton case (${\cal N}=4$ super Yang-Mills theory). Thermodynamics of obtained backgrounds is studied. In particular, next-to-leading term to free energy F is evaluated as $F=-{\tilde V_3 \over 4\pi^2}({N^2 (\pi T)^4 \over 2} + {5c^2 \over 768 g_{YM}^6 N{\alpha'}^6 (\pi T)^4})$. Here $\tilde V_3$ is the volume of the space part in the boundary of AdS, c is the parameter coming from the non-constant dilaton and N is the number of the coincident D3-branes.

Supersymmetry and electroweak breaking from extra dimensions at the TeV scale

We analyze some features of the role that extra dimensions, of radius $R$ in the TeV$^{-1}$ range, can play in the soft breaking of supersymmetry and the spontaneous breaking of electroweak symmetry. We use a minimal model where the gauge and Higgs sector of the MSSM are living in the bulk of five dimensions and the chiral multiplets in a four-dimensional boundary. Supersymmetry is broken in the bulk by the Scherk-Schwarz mechanism and transmitted to the boundary by radiative corrections. The particle spectrum is completely predicted as a function of a unique $R$-charge. The massless sector corresponds to the pure Standard Model and electroweak symmetry is radiatively broken with a light Higgs weighing $\simlt$ 110 GeV. The $\mu$-problem is solved and Higgsinos, gauginos and heavy Higgses acquire masses $\sim 1/R$. Chiral sfermions acquire radiative squared-masses $\sim \alpha_i/R^2$. The effective potential is explicitly computed in the bulk of extra dimensions and some cosmological consequences can be immediately drawn from it. Gauge coupling running and unification is studied in the presence of Scherk-Schwarz supersymmetry breaking. The unification is similar to that in the supersymmetric theory.

Gauge coupling instability and dynamical mass generation in N=1 three-dimensional supersymmetric QED

Using superfield Dyson-Schwinger equations, we compute the infrared dynamics of the semi-amputated full vertex, corresponding to the effective running gauge coupling, in N-flavour {\mathcal N}=1 supersymmetric QED(3). It is shown that the presence of a supersymmetry-preserving mass for the matter multiplet stabilizes the infrared gauge coupling against oscillations present in the massless case, and we therefore infer that the massive vacuum is thus selected at the level of the (quantum) effective action. We further demonstrate that such a mass can indeed be generated dynamically in a self-consistent way by appealing to the superfield Dyson-Schwinger gap equation for the full matter propagator.

Running gauge coupling and quark–antiquark potential from dilatonic gravity

The running gauge coupling and quark–antiquark potential in d-dimensions are calculated from the explicit solution of d+1-dimensional dilatonic gravity. This background interpolates between usual AdS in UV and flat space with singular dilaton in IR and it realizes two-boundaries AdS/CFT correspondence. The behaviour of running coupling and potential is consistent with results following from IIB supergravity.

Field strength correlator and an infrared fixed point of the Wilsonian exact renormalization group equations

The correlator of two field strengths is computed from an effective action for Yang Mills theories, which contains both gluons and an auxiliary antisymmetric tensor field for the field strength as local variables. This action allows to relate explicitly many different approaches to confinement, and is computed using Wilsonian renormalization group equations with the bare Yang Mills action as starting point. Due to the inclusion of a higher dimensional operator in the ghost sector the running gauge coupling becomes vanishingly small at a critical scale kc, and the resulting low energy action resembles the action of a confining string theory proposed by Polyakov.

The Higgs boson mass and Ward-Takahashi identity in gauged Nambu-Jona-Lasinio model

A new formula for the composite Higgs boson mass is given, based on the Ward-Takahashi identity and the Schwinger-Dyson(SD) equation. In this formula the dominant asymptotic solution of the SD equation yields a correct answer, in sharp contrast to the Partially Conserved Dilatation Current(PCDC) approach where the sub- and sub-sub-dominant solutions should be taken into account carefully. In the gauged Nambu-Jona-Lasinio model we find M H≃ 2 M for the composite Higgs boson mass M H and the dynamical mass of the fermion M in the case of the constant gauge coupling(with large cut off), which is consistent with the PCDC approach and the renormalization-group approach. As to the case of the running gauge coupling, we find M H≃2 (A−1)/(2A−1) M (A>1,Λ→∞) , where A≡18 C 2/(11 N c −2 N f ) with C 2 being the quadratic Casimir of the fermion representation. We also discuss a straightforward application of our formula to QCD(without 4-Fermi coupling), which yields M σ∼ 2 M dyn , with M σ and M dyn being the light scalar(“ σ-meson”) mass and mass of the constituent quark, respectively.

Gauge theories from orientifolds and large- N limit

Extending the recent work by M. Bershadsky, Z. Kakushadze and C. Vafa (hep-th/9803076), we consider string perturbative expansion in the presence of D-branes and orientifold planes imbedded in orbifolded space-time. In the α′ → 0 limit the weak coupling string perturbative expansion maps to `t Hooft's large- N expansion. We focus on four-dimensional N = 1, 2, 4 supersymmetric theories, and also discuss possible extensions to N = 0 cases. Utilizing the string theory perturbation techniques we show that computation of any M-point correlation function in these theories reduces to the corresponding computation in the parent N = 4 theory. In particular, we discuss theories (which are rather constrained) with vanishing β-functions to all orders in perturbation theory in the large- N limit. We also point out that in theories with non-vanishing β-functions the gauge coupling running is suppressed in the large- N limit. Introduction of orientifold planes allows to construct certain gauge theories with SO, Sp and SU gauge groups and various matter (only unitary gauge groups with bi-fundamental/adjoint matter arise in theories without orientifold planes).

Unification picture in the minimal supersymmetricSU(5)model with string remnants

The significant heavy threshold effect is found in the minimal supersymmetric $\mathrm{SU}(5)$ model with two adjoint scalars, one of which is interpreted as a massive string mode largely decoupled from the lower-energy particle spectra. This threshold related with the generic mass splitting of the basic adjoint moduli is shown to alter properly the running of gauge couplings, thus giving a natural solution to the string-scale grand unification. The further symmetry condition of the (top-bottom) Yukawa and gauge coupling superunification at a string scale results in the perfectly working predictions for the top and bottom quark masses in the absence of any large supersymmetric threshold corrections.

Field strength correlator and an infrared fixed point of the Wilsonian exact renormalization group equations

The correlator of two field strengths is computed from an effective action for Yang Mills theories, which contains both gluons and an auxiliary antisymmetric tensor field for the field strength as local variables. This action allows to relate explicitly many different approaches to confinement, and is computed using Wilsonian renormalization group equations with the bare Yang Mills action as starting point. Due to the inclusion of a higher dimensional operator in the ghost sector the running gauge coupling becomes vanishingly small at a critical scale k_c, and the resulting low energy action resembles the action of a confining string theory proposed by Polyakov.

The BFKL pomeron with running coupling constant: how much of its hard nature survives?

We discuss the BFKL equation with a running gauge coupling and identify in its solutions the contributions originating from different transverse momentum scales. We show that for a running coupling constant the distribution of the gluons making up the BFKL Pomeron shifts to smaller transverse momenta so that the dominant part of Pomeron can have a non-perturbative origin. It is demonstrated how this soft physics enters into the BFKL solution through the boundary condition. We consider two kinematical regimes leading to different behaviour of the rapidity and transverse momentum dependence of the gluon distribution. In the diffusion approximation to the BFKL kernel with running α s , we find a sequence of poles which replaces the cut for fixed α s . The second regime corresponds to the singular part of the kernel, which gives the dominant contribution in the limit of very large transverse momenta. Finally, a simple more general picture is obtained for the QCD Pomeron in hard processes: it is of soft, non-perturbative nature, but has hard ends of DGLAP type.

Nonperturbative Flow Equations in QCD

We review the formalism of the effective average action in quantum field theory which corresponds to a coarse grained free energy in statistical mechanics. The associated exact renormalization group equation and possible nonperturbative approximations for its solution are discussed. This is applied to QCD where one observes the consecutive emergence of mesonic bound states and spontaneous chiral symmetry breaking as the coarse graining scale is lowered. We finally present a study of the chiral phase transition in two flavor QCD. A precision estimate of the universal critical equation of state for the three-dimensional 0( 4) Heisenberg model is presented. We explicitly connect the 0( 4) universal behavior near the critical temperature and zero quark mass with the physics at zero temperature and a realistic pion mass. For realistic quark masses the pion correlation length near Tc turns out to be smaller than its zero temperature value. Quantum chromodynamics (QCD) describes qualitatively different physics at different length scales. At short distances the relevant degrees of freedom are quarks and gluons which can be treated perturbatively. At long distances we observe hadrons, and an essential part of the dynamics can be encoded in the masses and interactions of mesons. Any attempt to deal with this situation analytically and to predict the meson properties from the short distance physics (as functions of the strong gauge coupling o: 8 and the current quark masses mq) has to bridge the gap between two qualitatively different effective descriptions. Two basic problems have to be mastered for an extrapolation from short distance QCD to mesonic length scales: • The effective couplings change with scale. This does not only concern the running gauge coupling, but also the coefficients of non-renormalizable opera­ tors as, for example, four quark operators. Typically, these non-renormalizable terms become important in the momentum range where 0:8 is strong and deviate substantially from their perturbative values. Consider the four-point function which results after integrating out the gluons. For heavy quarks it contains the information about the shape of the heavy quark potential whereas for light quarks the complicated spectrum of light mesons and chiral symmetry breaking are encoded in it. At distance scales around 1 fm one expects that the effec­ tive action resembles very little the form of the classical QCD action which is relevant at short distances. • Not only the couplings, but even the relevant variables or degrees of freedom are different for long distance and short distance QCD. It seems forbiddingly

The running gauge coupling in the exact renormalization group approach

We discuss the perturbative running Yang-Mills coupling constant in the Wilsonian exact renormalization group approach, and compare it to the running coupling in the more conventional MS scheme. The exact renormalization group approach corresponds to a particular renormalization scheme, and we relate explicitly the corresponding Λ parameters. The unambiguous definition of an exact renormalization group scheme requires, however, the use of a one-loop improved high energy effective action.

Predictions ofmb/mτandmtin an asymptotically nonfree theory

We discuss an extension of the minimal supersymmetric standard model with five generations of matter superfields. The extra generations are assumed to form a generation--mirror-generation pair (the fourth and antifourth generations) enabling the extra fermions to have $\mathrm{SU}{(2)}_{L}\ifmmode\times\else\texttimes\fi{}\mathrm{U}{(1)}_{Y}$-invariant masses. Because of the contribution of the extra generations, all three running gauge couplings of $\mathrm{SU}{(3)}_{C}\ifmmode\times\else\texttimes\fi{}\mathrm{SU}{(2)}_{L}\ifmmode\times\else\texttimes\fi{}\mathrm{U}{(1)}_{Y}$ become asymptotically nonfree while preserving gauge coupling unification at the grand unified theory (GUT) scale. We show that, due to the asymptotically nonfree character of the gauge couplings, (1) the top and bottom Yukawa couplings are strongly focused onto infrared fixed points as they are evolved down in scale making their values at $\ensuremath{\mu}{=M}_{Z}$ insensitive to their initial values at $\ensuremath{\mu}{=M}_{\mathrm{GUT}},$ (2) the model predicts ${R}_{b\ensuremath{\tau}}{(M}_{Z})\ensuremath{\equiv}{Y}_{b}{/Y}_{\ensuremath{\tau}}{|}_{\ensuremath{\mu}{=M}_{Z}}\ensuremath{\approx}1.8$, which is consistent with the experimental value provided we take the ratio of Yukawa couplings at the GUT scale to be ${R}_{b\ensuremath{\tau}}{(M}_{\mathrm{GUT}}{)=Y}_{b}{/Y}_{\ensuremath{\tau}}{|}_{\ensuremath{\mu}{=M}_{\mathrm{GUT}}}=1/3$, and (3) the $t$ mass prediction comes out to be ${m}_{t}$\ensuremath{\approx}180 GeV which is also consistent with experiment.

Gauge coupling unification in GUT and string models

The results for the running of gauge couplings in the MSSM are updated by proper inclusion of all low scale effects. They are presented as predictions for the strong coupling constant in the scenario with only two parameters at the GUT scale ( α U and M U ) and as a mismatch of the couplings at the scales ∼ 3 × 10 16 GeV and 4 × 10 17 GeV, when all three couplings are taken as the experimental input.