12 research outputs found
The Phase Diagram for Wess-Zumino Models
Dynamical supersymmetry breaking is an important issue for applications of
supersymmetry in particle physics. The functional renormalization group
equations allow for a nonperturbative approach that leaves supersymmetry
intact. Therefore they offer a promising tool to investigate dynamical
supersymmetry breaking. Here we will employ this method to derive the phase
diagram and a surprisingly rich RG fixed-point structure with corresponding
critical exponents for the Wess-Zumino model in two dimensions.Comment: 4 pages, 4 figures, talk given at SUSY09, Boston, MA, 5-10 June 2009,
to appear in the proceeding
Functional Renormalisation Group Equitions for Supersymmetric Field Theories
Die Dissertation beschäftigt sich mit der Anwendung der funktionalen Renormierungsgruppe (FRG) auf supersymmetrische Feldtheorien. Es werden Skalarfeldtheorien in verschiedenen Dimensionen untersucht und eine Formulierung der Flussgleichung demonstriert, die manifest supersymmetrisch ist. Dies führt auf Ebene der Komponenten zu einer engen Verflechtung von bosonischen und fermionischen Regulatoren und erzwingt eine Regulatorstruktur, welche von der abweicht, die in Theorien mit Yukawa-Wechselwirkungen ohne Supersymmetrie benutzt wird.
Mit dieser Methode werden die supersymmetrische Quantenmechanik, das N=1 Wess-Zumino Modell in zwei und drei Dimensionen sowie das N=2 Wess-Zumino Modell in zwei Dimensionen untersucht. Anhand der supersymmetrischen Quantenmechanik wird demonstriert, dass die supersymmetrische Formulierung der Flussgleichung in der Lage ist, bekannte Ergebnisse korrekt zu reproduzieren. Desweiteren werden die Grenzen der betrachteten Näherungen aufgezeigt und diskutiert. Im Rahmen des N=1 Wess-Zumino Modells in zwei und drei Dimensionen, welches spontane Supersymmetriebrechung zeigt, wird das Phasendiagramm für die Supersymmetriebrechung berechnet sowie die Fixpunktstruktur des Renormierungsgruppenflusses untersucht. Hierbei ergibt sich eine neue Skalenrelation zwischen den kritischen Exponenten. Das dreidimensionale Modell wird ausserdem bei endlichen Temperaturen untersucht. Für das N=2 Wess-Zumino Modell in zwei Dimensionen, in dem Supersymmetrie nicht gebrochen werden kann, erlaubt die FRG eine sehr einfache Formulierung des Nichtrenormierungstheorems für das Superpotential. Da das Modell endlich ist, lässt sich die Renormierung der Masse des Skalarfeldes direkt mit Resultaten aus Monte-Carlo Simulationen auf dem Gitter vergleichen. Dies erlaubt eine Abschätzung der Genauigkeit der verwendeten Näherung
Supersymmetry breaking as a quantum phase transition
We explore supersymmetry breaking in the light of a rich fixed-point
structure of two-dimensional supersymmetric Wess-Zumino models with one
supercharge using the functional renormalization group (RG). We relate the
dynamical breaking of supersymmetry to an RG relevant control parameter of the
superpotential which is a common relevant direction of all fixed points of the
system. Supersymmetry breaking can thus be understood as a quantum phase
transition analogously to similar transitions in correlated fermion systems.
Supersymmetry gives rise to a new superscaling relation between the critical
exponent associated with the control parameter and the anomalous dimension of
the field -- a scaling relation which is not known in standard spin systems.Comment: 5 pages, 2 figures, discussion of results extended, version to appear
as a Rapid Communication in Phys. Rev.
Critical behavior of supersymmetric O(N) models in the large-N limit
We derive a supersymmetric renormalization group (RG) equation for the
scale-dependent superpotential of the supersymmetric O(N) model in three
dimensions. For a supersymmetric optimized regulator function we solve the RG
equation for the superpotential exactly in the large-N limit. The fixed-point
solutions are classified by an exactly marginal coupling. In the weakly coupled
regime there exists a unique fixed point solution, for intermediate couplings
we find two separate fixed point solutions and in the strong coupling regime no
globally defined fixed-point potentials exist. We determine the exact critical
exponents both for the superpotential and the associated scalar potential.
Finally we relate the high-temperature limit of the four-dimensional theory to
the Wilson-Fisher fixed point of the purely scalar theory.Comment: 13 pages,4 figure
Relation between chiral symmetry breaking and confinement in YM-theories
Spectral sums of the Dirac-Wilson operator and their relation to the Polyakov
loop are thoroughly investigated. The approach by Gattringer is generalized to
mode sums which reconstruct the Polyakov loop locally. This opens the
possibility to study the mode sum approximation to the Polyakov loop
correlator. The approach is re-derived for the ab initio continuum formulation
of Yang-Mills theories, and the convergence of the mode sum is studied in
detail. The mode sums are then explicitly calculated for the Schwinger model
and SU(2) gauge theory in a homogeneous background field. Using SU(2) lattice
gauge theory, the IR dominated mode sums are considered and the mode sum
approximation to the static quark anti-quark potential is obtained numerically.
We find a good agreement between the mode sum approximation and the static
potential at large distances for the confinement and the high temperature
plasma phase.Comment: 17 pages, 10 figures, typos corrected, references added, final
version to appear in PR
Flow Equation for Supersymmetric Quantum Mechanics
We study supersymmetric quantum mechanics with the functional RG formulated
in terms of an exact and manifestly off-shell supersymmetric flow equation for
the effective action. We solve the flow equation nonperturbatively in a
systematic super-covariant derivative expansion and concentrate on systems with
unbroken supersymmetry. Already at next-to-leading order, the energy of the
first excited state for convex potentials is accurately determined within a 1%
error for a wide range of couplings including deeply nonperturbative regimes.Comment: 24 pages, 8 figures, references added, typos correcte
The two dimensional N=(2,2) Wess-Zumino model in the functional renormalization group approach
We study the supersymmetric N=(2,2) Wess-Zumino model in two dimensions with the functional renormalization group. At leading order in the supercovariant derivative expansion we recover the nonrenormalization theorem which states that the superpotential has no running couplings. Beyond leading order the renormalization of the bare mass is caused by a momentum dependent wave function renormalization. To deal with the partial differential equations we have developed a numerical toolbox called FlowPy. For weak couplings the quantum corrections to the bare mass found in lattice simulations is reproduced with high accuracy. But in the regime with intermediate couplings higher-order-operators that are not constrained by the nonrenormalization theorem yield the dominating contribution to the renormalized mas