605 research outputs found
Koebe 1/4-Theorem and Inequalities in N=2 Super-QCD
The critical curve on which ,
, determines hyperbolic domains whose Poincar\'e metric is
constructed in terms of and . We describe in a parametric
form related to a Schwarzian equation and prove new relations for Super
Yang-Mills. In particular, using the Koebe 1/4-theorem and Schwarz's
lemma, we obtain inequalities involving , and , which seem related
to the Renormalization Group. Furthermore, we obtain a closed form for the
prepotential as function of . Finally, we show that , where is the one-loop coefficient of the beta
function.Comment: 11 pages, LaTex file, Expanded version: new results, technical
details explained, misprints corrected and references adde
Noncommutative Riemann Surfaces
We compactify M(atrix) theory on Riemann surfaces Sigma with genus g>1.
Following [1], we construct a projective unitary representation of pi_1(Sigma)
realized on L^2(H), with H the upper half-plane. As a first step we introduce a
suitably gauged sl_2(R) algebra. Then a uniquely determined gauge connection
provides the central extension which is a 2-cocycle of the 2nd Hochschild
cohomology group. Our construction is the double-scaling limit N\to\infty,
k\to-\infty of the representation considered in the Narasimhan-Seshadri
theorem, which represents the higher-genus analog of 't Hooft's clock and shift
matrices of QCD. The concept of a noncommutative Riemann surface Sigma_\theta
is introduced as a certain C^\star-algebra. Finally we investigate the Morita
equivalence.Comment: LaTeX, 1+14 pages. Contribution to the TMR meeting ``Quantum aspects
of gauge theories, supersymmetry and unification'', Paris 1-7 September 199
Nonperturbative Relations in N=2 SUSY Yang-Mills and WDVV equation
We find the nonperturbative relation between , the prepotential and the
vevs in supersymmetric Yang-Mills theories with
gauge group . Nonlinear differential equations for including
the Witten -- Dijkgraaf -- Verlinde -- Verlinde equation are obtained. This
indicates that SYM theories are essentially topological field theories
and that should be seen as low-energy limit of some topological string theory.
Furthermore, we construct relevant modular invariant quantities, derive
canonical relations between the periods and investigate the structure of the
beta function by giving its explicit form in the moduli coordinates. In doing
this we discuss the uniformization problem for the quantum moduli space. The
method we propose can be generalized to supersymmetric Yang-Mills
theories with higher rank gauge groups.Comment: 12 pages, LaTex. Expanded version. New results, corrections,
references and acknowledgements adde
The Relativistic Quantum Motions
Using the relativistic quantum stationary Hamilton-Jacobi equation within the
framework of the equivalence postulate, and grounding oneself on both
relativistic and quantum Lagrangians, we construct a Lagrangian of a
relativistic quantum system in one dimension and derive a third order equation
of motion representing a first integral of the relativistic quantum Newton's
law. Then, we plot the relativistic quantum trajectories of a particle moving
under the constant and the linear potentials. We establish the existence of
nodes and link them to the de Broglie's wavelength.Comment: Latex, 18 pages, 3 eps figure
Benefits of Artificially Generated Gravity Gradients for Interferometric Gravitational-Wave Detectors
We present an approach to experimentally evaluate gravity gradient noise, a
potentially limiting noise source in advanced interferometric gravitational
wave (GW) detectors. In addition, the method can be used to provide sub-percent
calibration in phase and amplitude of modern interferometric GW detectors.
Knowledge of calibration to such certainties shall enhance the scientific
output of the instruments in case of an eventual detection of GWs. The method
relies on a rotating symmetrical two-body mass, a Dynamic gravity Field
Generator (DFG). The placement of the DFG in the proximity of one of the
interferometer's suspended test masses generates a change in the local
gravitational field detectable with current interferometric GW detectors.Comment: 16 pages, 4 figure
Algebraic-geometrical formulation of two-dimensional quantum gravity
We find a volume form on moduli space of double punctured Riemann surfaces
whose integral satisfies the Painlev\'e I recursion relations of the genus
expansion of the specific heat of 2D gravity. This allows us to express the
asymptotic expansion of the specific heat as an integral on an infinite
dimensional moduli space in the spirit of Friedan-Shenker approach. We outline
a conjectural derivation of such recursion relations using the
Duistermaat-Heckman theorem.Comment: 10 pages, Latex fil
Nonperturbative Renormalization Group Equation and Beta Function in N=2 SUSY Yang-Mills
We obtain the exact beta function for SUSY Yang-Mills theory
and prove the nonperturbative Renormalization Group Equation Comment: LaTex, 10 pg. Expanded introduction, references added, to appear in
Phys. Rev. Let
RG Flow Irreversibility, C-Theorem and Topological Nature of 4D N=2 SYM
We determine the exact beta function and a RG flow Lyapunov function for N=2
SYM with gauge group SU(n). It turns out that the classical discriminants of
the Seiberg-Witten curves determine the RG potential. The radial
irreversibility of the RG flow in the SU(2) case and the non-perturbative
identity relating the -modulus and the superconformal anomaly, indicate the
existence of a four dimensional analogue of the c-theorem for N=2 SYM which we
formulate for the full SU(n) theory. Our investigation provides further
evidence of the essentially topological nature of the theory.Comment: 9 pages, LaTeX file. Discussion on WDVV and integrability. References
added. Version published in PR
On the Relation Between the Holomorphic Prepotential and the Quantum Moduli in SUSY Gauge Theories
We give a simple proof of the relation \Lambda\p_artial{\Lambda}\F=
{i\over2\pi}b_1\langle\Tr\phi^2\rangle, which is valid for
supersymmetric QCD with massless quarks. We consider gauge theories
as well as and . Aa analogous relation which corresponds to
massive hypermultiplets is written down. We also discuss the generalizations to
models in the Coulomb phase.Comment: 9 pages, harvma
Non-holomorphic terms in N=2 SUSY Wilsonian actions and RG equation
In this paper we first investigate the Ansatz of one of the present authors
for K(\Psi,\bar\Psi), the adimensional modular invariant non-holomorphic
correction to the Wilsonian effective Lagrangian of an N=2 globally
supersymmetric gauge theory. The renormalisation group beta-function of the
theory crucially allows us to express K(\Psi,\bar\Psi) in a form that easily
generalises to the case in which the theory is coupled to N_F hypermultiplets
in the fundamental representation of the gauge group. This function satisfies
an equation which should be viewed as a fully non-perturbative ``non-chiral
superconformal Ward identity". We also determine its renormalisation group
equation. Furthermore, as a first step towards checking the validity of this
Ansatz, we compute the contribution to K(\Psi,\bar\Psi) from instantons of
winding number k=1 and k=2. As a by-product of our analysis we check a
non-renormalisation theorem for N_F=4.Comment: 39 pages, LaTex file, no figure
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