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 $\mathcal N=1$ 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