1,721,078 research outputs found
The Nicolai Map and its Application in Supersymmetric Field Theories
Full text linkSupersymmetrische Feldtheorien können durch eine nicht-lineare und nicht-lokale Transformation der bosonischen Felder charakterisiert werden, der Nicolai-Abbildung. Sie bildet das wechselwirkende Funktionalmaß so auf das Maß der zugehörigen freien Theorie ab, dass die Jacobi-Determinante gleich dem Produkt der fermionischen Determinanten ist. Wir untersuchen die Nicolai-Abbildungen des 2-dimenionalen Wess-Zumino Modells und der N=1 sowie N=4 super Yang-Mills Theorien. Wir geben einen konstruktiven Beweis für die Existenz der Nicolai-Abbildung in diesen Theorien. Der Beweis beinhaltet die Herleitung des infinitesimalen Generators der inversen Abbildung, dem R-Operator. Wir benutzen diesen Operator, um die Nicolai-Abbildung im 2-dimensionalen Wess-Zumino Modell bis zur fünften Ordnung in der Kopplung zu berechnen. In der N=1 super Yang-Mills Theorie führen wir die Begriffe der on- bzw. off-shell Nicolai-Abbildungen ein. Die on-shell Abbildung existiert in d=3,4,6 und 10 Dimensionen aber nur für die Landau Eichung. Wir bestimmen sie bis zur vierten Ordnung. Die off-shell Abbildung existiert nur in d=4 Dimensionen aber für allgemeine Eichungen. Wir berechnen sie in der axialen Eichung bis zur zweiten Ordnung. Für die N=4 super Yang-Mills Theorie geben wir den R-Operator an und zeigen, dass man die N=4 Nicolai-Abbildung durch dimensionale Reduktion aus der N=1 Abbildung erhält. Inverse Nicolai-Abbildungen bilden Quantenkorrelationsfunktionen bosonischer Observablen auf freie Korrelationsfunktionen ab. Daher gestatten sie eine Quantisierung supersymmetrischer Theorien ohne die Verwendung von Fermionen oder Geistern. Wir benutzten diese Eigenschaft, um den Vakuum-Erwartungswert der Maldacena-Wilson Geraden bis zur sechsten Ordnung zu berechnen. Im zweiten Teil dieser Arbeit bestimmen wir die explizite Form aller Felder im 1/2-BPS Energie-Impuls-Tensor Multiplet in N=4 super Yang-Mills. Dieses Multiplet enthält den R-Symmetrie Fluss und den Energie-Impuls-Tensor.Supersymmetric field theories can be characterized by the existence of a non-linear and non-local transformation of the bosonic fields, the Nicolai map. It maps the interacting functional measure to that of a free theory such that the Jacobian determinant of the transformation equals the product of the fermionic determinants. In this thesis, we study the Nicolai maps of the 2-dimensional Wess-Zumino model, N=1 super Yang-Mills and N=4 super Yang-Mills. We give a constructive proof for the existence of the Nicolai map in these theories. The proof includes the derivation of the infinitesimal generator of the inverse Nicolai map, called the R-operator. We use this operator to compute the Nicolai map of the 2-dimensional Wess-Zumino model up to the fifth order in the coupling. In N=1 super Yang-Mills, we introduce the notion of on- and off-shell Nicolai maps. The on-shell Nicolai map of N=1 super Yang-Mills exists in d=3,4,6 and 10 dimensions but is constrained to the Landau gauge. We compute this map up to the fourth order. The off-shell Nicolai map exists only in d=4 dimensions but for general gauges. We compute it in the axial gauge up to the second order. In N=4 super Yang-Mills, we give the R-operator and show that the Nicolai map can be obtained from the Nicolai map of 10-dimensional N=1 super Yang-Mills by dimensional reduction. Inverse Nicolai maps map quantum correlation functions of bosonic observables to free correlation functions. Hence, Nicolai maps allow for a fermion (and ghost) free quantization of supersymmetric (gauge) theories. We apply this property to compute the vacuum expectation value of the infinite straight line Maldacena-Wilson loop in N=4 super Yang-Mills to the sixth order. Thus extending the previous perturbative result by one order. In the second part of this thesis, we derive the explicit field content of the 1/2-BPS stress tensor multiplet in N=4 super Yang-Mills, which contains the R-symmetry current and the energy-momentum tensor
Superstring limit of Yang–Mills theories
Full text linkAbstractIt was pointed out by Shifman and Yung that the critical superstring on X10=R4×Y6, where Y6 is the resolved conifold, appears as an effective theory for a U(2) Yang–Mills–Higgs system with four fundamental Higgs scalars defined on Σ2×R2, where Σ2 is a two-dimensional Lorentzian manifold. Their Yang–Mills model supports semilocal vortices on R2⊂Σ2×R2 with a moduli space X10. When the moduli of slowly moving thin vortices depend on the coordinates of Σ2, the vortex strings can be identified with critical fundamental strings. We show that similar results can be obtained for the low-energy limit of pure Yang–Mills theory on Σ2×Tp2, where Tp2 is a two-dimensional torus with a puncture p. The solitonic vortices of Shifman and Yung then get replaced by flat connections. Various ten-dimensional superstring target spaces can be obtained as moduli spaces of flat connections on Tp2, depending on the choice of the gauge group. The full Green–Schwarz sigma model requires extending the gauge group to a supergroup and augmenting the action with a topological term
Noncommutative deformation of the Ward metric
No full textThe moduli-space metric in the static non-Abelian charge-two sector of the Moyal-deformed CP1 sigma model in 1+2 dimensions is analyzed. After recalling the commutative results of Ward and Ruback and the ?-regularized construction of the noncommutative Kahler potential due to the second author, explicit expressions and asymptotics for it are presented and discussed in different regions of the moduli space. Along two curves in the moduli space the potential can be calculated analytically. In the region of solitons known as "ring-like", perturbation theory is used. In the region of "lump-like" solitons, both perturbation theory and the z -function approach are employed. While the strong noncommutativity limit is smooth and under control, the commutative limit in the two-lump region remains a semiclassical challenge
Noncommutative deformation of the Ward metric
No full textThe moduli-space metric in the static non-Abelian charge-two sector of the Moyal-deformed CP1 sigma model in 1+2 dimensions is analyzed. After recalling the commutative results of Ward and Ruback and the ζ-regularized construction of the noncommutative Kahler potential due to the second author, explicit expressions and asymptotics for it are presented and discussed in different regions of the moduli space. Along two curves in the moduli space the potential can be calculated analytically. In the region of solitons known as "ring-like", perturbation theory is used. In the region of "lump-like" solitons, both perturbation theory and the ζ-function approach are employed. While the strong noncommutativity limit is smooth and under control, the commutative limit in the two-lump region remains a semiclassical challenge
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Full text linkWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
The Nicolai-map approach to supersymmetry
Full text linkIn 1980 Hermann Nicolai proposed a characterization of supersymmetric
theories that became known as the Nicolai map. This is a particular nonlocal
and nonlinear field transformation, whose perturbative expansion is given by
fermion-line trees with bosonic leaves. Quantum correlation functions can by
evaluated using the inversely transformed fields in the free theory. After
initial promise and excitement (fuelling the author's PhD work!), the subject
all but fell dormant for 35 years. Recently however, technical progress in the
construction as well as a deeper insight into the nature of the map have been
achieved, from quantum mechanics to super Yang-Mills in various dimensions. I
will present the Nicolai map from this modern perspective and touch on some of
the current developments.Comment: 10 pages LaTeX; plenary talk at the XII. International Symposium on
Quantum Theory and Symmetries (QTS12), Prague, Czech Republic, 24-28 July
2023. arXiv admin note: text overlap with arXiv:2204.0209
The Nicolai-map approach to supersymmetry
Full text linkIn 1980 Hermann Nicolai proposed a characterization of supersymmetric theories that became known as the Nicolai map. This is a particular nonlocal and nonlinear field transformation, whose perturbative expansion is given by fermion-line trees with bosonic leaves. Quantum correlation functions can by evaluated using the inversely transformed fields in the free theory. After initial promise and excitement (fuelling the author's PhD work!), the subject all but fell dormant for 35 years. Recently however, technical progress in the construction as well as a deeper insight into the nature of the map have been achieved, from quantum mechanics to super Yang–Mills in various dimensions. I will present the Nicolai map from this modern perspective and touch on some of the current developments
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