Effective Actions and Gauge Field Stability

By studying an effective action description of the coupling of charged gauge fields in N=2 SU(n) supersymmetric Yang-Mills theories, we can describe regions of moduli space where one or more of these fields becomes unphysical. We discuss subtleties in the structure of the moduli space for SU(3).Comment: 13 pages, latex, no figure

On gauged linear sigma models with torsion

We study a broad class of two dimensional gauged linear sigma models (GLSMs) with off-shell N=(2,2) supersymmetry that flow to nonlinear sigma models (NLSMs) on noncompact geometries with torsion. These models arise from coupling chiral, twisted chiral, and semichiral multiplets to known as well as to a new N=(2,2) vector multiplet, the constrained semichiral vector multiplet (CSVM). We discuss three kinds of models, corresponding to torsionful deformations of standard GLSMs realizing Kahler, hyperkahler, and Calabi-Yau manifolds. The (2,2) supersymmetry guarantees that these spaces are generalized Kahler. Our analysis of the geometric structure is performed at the classical level, but we also discuss quantum aspects such as R-symmetry anomalies. We provide an explicit example of a generalized Kahler structure on the conifold.Comment: 39 pages, 1 figure. v2: References adde

Chromatic Polynomials for J(∏H)IJ(\prod H)I Strip Graphs and their Asymptotic Limits

We calculate the chromatic polynomials $P$ for $n$-vertex strip graphs of the form $J(\prod_{\ell=1}^m H)I$, where $J$ and $I$ are various subgraphs on the left and right ends of the strip, whose bulk is comprised of $m$-fold repetitions of a subgraph $H$. The strips have free boundary conditions in the longitudinal direction and free or periodic boundary conditions in the transverse direction. This extends our earlier calculations for strip graphs of the form $(\prod_{\ell=1}^m H)I$. We use a generating function method. From these results we compute the asymptotic limiting function $W=\lim_{n \to \infty}P^{1/n}$; for $q \in {\mathbb Z}_+$ this has physical significance as the ground state degeneracy per site (exponent of the ground state entropy) of the $q$-state Potts antiferromagnet on the given strip. In the complex $q$ plane, $W$ is an analytic function except on a certain continuous locus ${\cal B}$. In contrast to the $(\prod_{\ell=1}^m H)I$ strip graphs, where ${\cal B}$ (i) is independent of $I$, and (ii) consists of arcs and possible line segments that do not enclose any regions in the $q$ plane, we find that for some $J(\prod_{\ell=1}^m H)I$ strip graphs, ${\cal B}$ (i) does depend on $I$ and $J$, and (ii) can enclose regions in the $q$ plane. Our study elucidates the effects of different end subgraphs $I$ and $J$ and of boundary conditions on the infinite-length limit of the strip graphs.Comment: 33 pages, Latex, 7 encapsulated postscript figures, Physica A, in press, with some typos fixe

Complex Structures, Duality, and WZW-Models in Extended Superspace

We find the complex structure on the dual of a complex target space. For $N=(2,2)$ systems, we prove that the space orthogonal to the kernel of the commutator of the left and right complex structures is {\em always} integrable, and hence the kernel is parametrized by chiral and twisted chiral superfield coordinates. We then analyze the particular case of $SU(2)\times SU(2)$, and are led to a new $N=2$ superspace formulation of the $SU(2)\times U(1)$ WZW-model.Comment: Latex, 16 pages. In this revised manuscript, we add a section and an author, and alter one of the conclusions of the pape

A note on the Seiberg-Witten solution of N=2 Super Yang-Mills Theory

We examine the Seiberg-Witten treatment of N=2 super Yang-Mills theory, and note that in the strong coupling region of moduli space, some massive particle excitations appear to have negative norm. We discuss the significance of our observation.Comment: 4 pages, latex, no figures. The discussion has been revise

Monsters in Medieval Imagination of British Isles

(česky) Předkládaná práce se zabývá otázkou, zdali křesťanská církev užívala příběhů obsahujících nestvůrné bytosti za účelem získání anglosaské společnosti pro novou víru. Tato otázka je rozebírána na příkladu interpretační a obsahové analýzy několika staroanglických textů z Nowellova Kodexu, a to heroicko-elegické básně Béowulf, cestopisného textu Dopisu Alexandra Aristotelovi, legendy o Životě svatého Kryštofa a bestiáře Liber Monstrorum, který jako jediný není součástí jmenovaného kodexu. První kapitola práce poskytuje stručný souhrn vnímání nestvůrných bytostí od pravěku do středověku. Další kapitola se zaměřuje na rozbor role hrdinů, přírody a vzdálenosti Britských ostrovů od tehdy vnímaného centra civilizovaného světa. Tato kapitola je potom uzavřena analýzou pohanských prvků básně Béowulf. Závěrečná kapitola se zaměřuje na pojetí nestvůrných bytostí v křesťanském prostředí a následné analýze vybraných staroanglických textů v křesťanské interpretační rovině. Práce dochází k závěru, že církev 6. až 10. století motivů monster neužívala cíleně. Naopak se ukazuje, že docházelo spíše k volnému prolínání germánských a křesťanských elementů a postupnému nahrazování těch germánských. Klíčová slova (česky) Monstra, Britské ostrovy, Středověká církev, Kázání, Christianizace, Imaginace, Severské mýty,...(anglicky) The main question of this thesis is whether the Christian church used stories containing monster beings with the aim of converting the Anglo-Saxon society to the new faith. This question is looked at through interpretative and content analysis of several Old English texts from the Nowell Codex. These are: the heroic-elegiac poem Béowulf, the travelogue The Letter of Alexander to Aristotle, the hagiographic text The Passion of St Christopher and the bestiary Liber Monstrorum, which is the only afore mentioned text not included in the Nowell Codex. The first chapter of this thesis provides a basic summary of the perception of monster beings from the prehistoric times to the Middle Ages. The next chapter analyses the role of the hero, nature and the distance of the British Isles from the centre of the World as perceived at the time. This chapter ends with the analysis of the pagan elements in the poem Béowulf. The last chapter focuses on the interpretations of monster beings in Christian settings and analyses the chosen Old English texts on a Christian interpretative level. The thesis arrives at the conclusion that the Church of the 6th to 10th century didn't use the motifs of various monsters on purpose. On the contrary, it seems that Germanic and Christian elements freely converged, and...Ústav světových dějinInstitute of General HistoryFilozofická fakultaFaculty of Art

Duality, Quotients, and Currents

We study the generalization of $R\to 1/R$ duality to arbitrary conformally invariant sigma models with an isometry. We show that any pair of dual sigma models can be represented as quotients of a self-dual sigma model obtained by gauging different combinations of chiral currents. This observation is used to clarify the interpretation of the generalized duality as a symmetry of conformal field theory. We extend these results to $N=2$ supersymmetric sigma models.Comment: 20 page