Thesis (Ph. D)--University of Rochester, 2009. / Includes abstract and vita. Includes bibliographical references. Digitized version available online via the Sibley Music Library, Eastman School of Music http://hdl.handle.net/1802/11067

Thesis (Ph. D.)--University of California, San Diego, 2003. / Vita. "Three related compositions written for string quartet, small ensemble (soprano, violin, viola, cello, flute, clarinet, piano) and percussion duo"--P. viii; 3rd work an open form composition. Also available on the World Wide Web. (Access restricted to UC campuses).

This dissertation is on a study of 2-string free tangle decompositions of knots with tunnel number two. As an application, we construct infinitely many counter-examples to a conjecture in the literature stating that the tunnel number of the connected sum of prime knots doesn't degenerate by more than one: t(K_1#K_2)≥ t(K_1)+t(K_2)-1, for K_1 and K_2 prime knots. We also study 2-string free tangle decompositions of links with tunnel number two and obtain an equivalent statement to the one on knots. Further observations on tunnel number and essential tangle decompositions are also made. / text

The object of this work is to exploit various constructions of string theory and M-theory to yield new insights into supersymmetric theories in both four and three dimensions. In 4d, we extend work on Seiberg-Witten theory to study and compute BPS spectra of the class of complete N = 2 theories. The approach we take is based on the program of geometric engineering, in which 4d theories are constructed from compactifications of type IIB strings on Calabi-Yau manifolds. In this setup, the natural candidates for BPS states are D3 branes wrapped on supersymmetric 3-cycles in the Calabi-Yau. Our study makes use of the mathematical structure of quivers, whose representation theory encodes the notion of stability of BPS particles. Except for 11 exceptional cases, all complete theories can be constructed by wrapping stacks of two M5 branes on Riemann surfaces. By exploring the connection between quivers and M5 brane theories, we develop a powerful algorithm for computing BPS spectra, and give an in-depth study of its applications. In particular, we compute BPS spectra for all asymptotically free complete theories, as well as an infinite set of conformal \(SU(2)^k\) theories with certain matter content. From here, we go on to apply the insight gained from our 4d study to 3d gauge theories. We consider the analog of the M5 brane construction in the case of 3d N = 2 theories: pairs of M5 branes wrapped on a 3-manifold. Using the ansantz of R-flow, we study 3-manifolds consisting of Riemann surfaces fibered over R. When the construction is non-singular, the resulting IR physics is described by a free abelian Chern-Simons theory. The mathematical data of a tangle captures the data of the gauge theory, and the Reidemeister equivalances on tangles correspond to dualities of physical descriptions. To obtain interacting matter, we allow singularities in the construction. By extending the tangle description to these singular cases, we find a set of generalized Reidemeister moves that capture non-trivial mirror symmetries of 3d gauge theories. These results give a geometric origin to these well-known 3d dualities. / Physics

Not available / text

As subcontractors, electrical contractors have been facing unfavorable environments, with problems such as constrained job site areas, schedule interference, and inefficient communication with other trades. To achieve desired goals more efficiently, electrical contractors require a more systematic and effective project management strategy. The primary goal of this research is to develop continuous task strings that pair pre-construction planning (PCP) with relevant project execution (PE) tasks in order for electrical contractors to achieve significantly better performance. Incorporating several statistical analyses, the research demonstrates the effects of continuous task strings on project performance in terms of cost and schedule success. The results reveal that the levels of task string usage are significantly correlated to project success. Moreover, task strings have significant leveraged effects on project performance: project performance can be improved by stringing together related PCP and PE tasks as opposed to performing either PCP or PE task individually. The research further suggests the specific high-value task strings that significantly increase the likelihood of achieving successful project outcomes. Ultimately, by elucidating the relationship between pre-construction planning and project execution tasks, the research can help electrical contractors accomplish significantly better performance through effective project management strategies. / text

Η παρούσα διπλωματική εργασία αποτελεί μια σύντομη εισαγωγή στη θεωρία των Χορδών, ενώ ιδιαίτερη έμαφαση έχει δοθεί στις D-Branes. Αρχικά παρουσιάζεται η κλασική μποζονική χορδή, καθώς και η κβάντωσή της. Στη συνέχεια περιγράφεται ο Τ-δυϊσμός και εισάγονται οι D-Branes στη θεωρία, των οποίων και αναλύονται τα βασικά χαρακτηριστικά, ενώ παρουσιάζεται και η δράση κοσμικού όγκου για την περιγραφή τους. Ακολουθεί μια συνοπτική περιγραφή των υπερσυμετρικών χορδών και των διαφορετικών θεωριών χορδών που προκύπτουν. Τέλος, παρουσιάζεται η γεωμετρία που παράγουν οι D-Branes, σε αναλογία με την αντίστοιχη των μελανών οπών, και περιγράφεται ο τρόπος με τον οπίο κατασκευάζονται extremal μελανές οπές στη θεωρία χορδών καθώς και η μικροσκοπική περιγραφή τους μέσω κατάλληλων διατάξεων από D-Branes. / This thesis consists of a short introduction to string theory, while emphasis has been given on D-Branes. First, the classical bosonic string is presented, and its quantization. T-duality is described and D-Branes are introduced in the theory, the basic properties of which are analyzed. A short discussion of supersymmetric strings follows. Finally, the geometry of D-branes is presented, with respect to the geometry of black holes, and the way that extremal black holes are constructed in string theory, while also their microscopic describtion in terms of D-branes.

Στόχος της διατριβής είναι η αναζήτηση υπερσυμμετρικών λύσεων με προέλευση από την Μ θεωρία και τη θεωρία χορδών στις 10-διαστάσεις, με συνακόλουθη μελέτη των συνεπειών τους στις 4-διαστάσεις μέσω της αντιστοιχίας βαρύτητας/βαθμίδας. Στο πρώτο βήμα προχωρούμε σε συστηματική κατασκευή υπερσυμμετρικών βαρυτικών λύσεων της υπερβαρύτητας σε διάφορες διαστάσεις με μειωμένη Lorentzian ολονομία. Η κατασκευή μας βασίζεται στην εισαγωγή χρονικής εξάρτησης στις παραμέτρους moduli των Riemannian αντιγράφων. Συνεπώς οδηγούμαστε σε D-διάστατες υπερσυμμετρικές λύσεις κενού με Lorentzian ομάδα ολονομίας της μορφής G×RD-2. Στο δεύτερο βήμα προσεγγίζουμε τους 5-διάστατους χώρους Sasaki-Einstein, οι οποίοι παρεμβάλονται μεταξύ της S5 και του T1,1. Χρησιμοποιώντας τους 5-διάστατους αυτούς χώρους σαν βάση κατασκευάζουμε 6-διάστατους υπερσυμμετρικούς κώνους, οι οποίοι στη συνέχεια θα αποτελέσουν τα δομικά στοιχεία για την κατασκευή λύσεων της 10-διάστατης υπερβαρύτητας τύπου ΙΙΒ για συσσωματώματα από D3 και D5-βράνες. Στο τρίτο βήμα μελετάμε τις δυϊκές βαρυτικές λύσεις του κλάδου Coulomb που αντιστοιχούν σε μια marginally παραμορφωμένη N=4 θεωρία Yang-Mills. Μέσα από μια αλληλουχία από Τ δυϊκότητες και μετατοπίσεις συντεταγμένων κατασκευάζουμε το δυϊκο βαρυτικό υπόβαθρο, ουσιαστικά παρουσιάζοντας μια γενική μεθοδολογία. Εξετάζουμε ενδελεχώς το ζήτημα της υπερσυμμετρίας και πως αυτή ελαττώνεται από Ν=4 σε Ν=1. Στη συνέχεια ανιχνεύουμε την γεωμετρία μέσα από τον υπολογισμό του βρόχου Wilson για ζεύγος βαρέων quark-antiquark, αποκαλύπτοντας φαινόμενα θωράκισης και εγκλωβισμού για το δυναμικό. / Our main objective is the quest of supersymmetric solutions coming from M theory and 10-dim string theory together with the study of their implications in 4-dim through the AdS/CFT correspondence. As a first step we proceed in a systematic construction of supersymmetric supergravity solutions in diverse dimensions with reduced Lorentzian holonomy. Our construction is based on time dependence insertion over the moduli parameters of the Riemannian counterparts. We end up with D-dim supersymmetric vacuum solutions with Lorentzian holonomy group of the semidirect product type G×RD-2. In the second step we get near the 5-dim Sasaki-Einstein spaces which interpolate between S5 and T1,1. Using those 5-dim spaces as a base we construct the 6-dim supersymmetric cones which in turn will form the building blocks for the consequent construction of supersymmetric type-IIB supergravity solutions representing a stack of D3- and D5-branes. In the last step we study the gravity duals of the Coulomb branch of marginally deformed N=4 Yang-Mills theory. Through a sequence of T dualities and coordinate shifts we construct the dual supergravity background, in other words present a general methodology. We examine in detail the issue of supersymmetry and in particular the way it is reduced from N=4 to N=1. We probe the geometry through the computation of the expectation value of the Wilson loop operator for a pair of quark-antiquark, reviling confining and complete screening phenomena for the potential.

In this thesis we investigate two different aspects of the AdS/CFT correspondence. We first investigate the holographic AdS/CMT correspondence. Gravitational backgrounds in d+2 dimensions have been proposed as holographic duals to Lifshitz-like theories describing critical phenomena in d+1 dimensions with critical exponent z>1. We numerically explore a dilaton-Einstein-Maxwell model admitting such backgrounds as solutions. We show how to embed these solutions into AdS space for a range of values of z and d. We next investigate the AdS3/CFT2 correspondence and focus on the microscopic CFT description of the D1-D5 system on T^4*S_1. In the context of the fuzzball programme, we investigate deforming the CFT away from the orbifold point and study lifting of the low-lying string states. We start by considering general 2D orbifold CFTs of the form M^N/S_N, with M a target space manifold and S_N the symmetric group. The Lunin-Mathur covering space technique provides a way to compute correlators in these orbifold theories, and we generalize this technique in two ways. First, we consider excitations of twist operators by modes of fields that are not twisted by that operator, and show how to account for these excitations when computing correlation functions in the covering space. Second, we consider non-twist sector operators and show how to include the effects of these insertions in the covering space. Using the generalization of the Lunin-Mathur symmetric orbifold technology and conformal perturbation theory, we initiate a program to compute the anomalous dimensions of low-lying string states in the D1-D5 superconformal field theory. Our method entails finding four-point functions involving a string operator O of interest and the deformation operator, taking coincidence limits to identify which other operators mix with O, subtracting conformal families of these operators, and computing their mixing coefficients. We find evidence of operator mixing at first order in the deformation parameter, which means that the string state acquires an anomalous dimension. After diagonalization this will mean that anomalous dimensions of some string states in the D1-D5 SCFT must decrease away from the orbifold point while others increase. Finally, we summarize our results and discuss some future directions of research.

In this thesis we investigate two different aspects of the AdS/CFT correspondence. We first investigate the holographic AdS/CMT correspondence. Gravitational backgrounds in d+2 dimensions have been proposed as holographic duals to Lifshitz-like theories describing critical phenomena in d+1 dimensions with critical exponent z>1. We numerically explore a dilaton-Einstein-Maxwell model admitting such backgrounds as solutions. We show how to embed these solutions into AdS space for a range of values of z and d. We next investigate the AdS3/CFT2 correspondence and focus on the microscopic CFT description of the D1-D5 system on T^4*S_1. In the context of the fuzzball programme, we investigate deforming the CFT away from the orbifold point and study lifting of the low-lying string states. We start by considering general 2D orbifold CFTs of the form M^N/S_N, with M a target space manifold and S_N the symmetric group. The Lunin-Mathur covering space technique provides a way to compute correlators in these orbifold theories, and we generalize this technique in two ways. First, we consider excitations of twist operators by modes of fields that are not twisted by that operator, and show how to account for these excitations when computing correlation functions in the covering space. Second, we consider non-twist sector operators and show how to include the effects of these insertions in the covering space. Using the generalization of the Lunin-Mathur symmetric orbifold technology and conformal perturbation theory, we initiate a program to compute the anomalous dimensions of low-lying string states in the D1-D5 superconformal field theory. Our method entails finding four-point functions involving a string operator O of interest and the deformation operator, taking coincidence limits to identify which other operators mix with O, subtracting conformal families of these operators, and computing their mixing coefficients. We find evidence of operator mixing at first order in the deformation parameter, which means that the string state acquires an anomalous dimension. After diagonalization this will mean that anomalous dimensions of some string states in the D1-D5 SCFT must decrease away from the orbifold point while others increase. Finally, we summarize our results and discuss some future directions of research.