Applications of Gauge/Gravity Duality to QCD and Heavy Ion Collisions

The description of quarks and gluons, using the theory of quantum chromodynamics (QCD), has been known for a long time. Nevertheless, many fundamental questions in QCD remain unanswered. This is mainly due to problems in solving the theory at low energies, where the theory is strongly interacting. AdS/CFT is a duality between a specific string theory and a conformal field theory. Duality provides new tools to solve the conformal field theory in the strong coupling regime. There is also some evidence that using the duality, one can get at least qualitative understanding of how QCD behaves at strong coupling. In this thesis, we try to address some issues related to QCD and heavy ion collisions, applying the duality in various ways.

Talousmetafysiikan kritiikkiä

Jakke Holvas: A Critique of the Metaphysics of Economy The research problem of this dissertation is the commonly held opinion according to which everything has become a question of economy in the present day. Economy legitimates and justifies. In this study, the pattern of thinking and conceptualizing in which economy figures as the ultimate reason is called the metaphysics of economy. The defining characteristic of the metaphysics of economy is its failure to recognize non-economic rules, ethics, or ways of existence. The sources included in the study cover certain classics of philosophy (Plato, Aristotle, Friedrich Nietzsche) and sociology (Karl Marx, Max Weber, Marcel Mauss), as well as the more recent French social theory (Jean Baudrillard, Michel Foucault). The research methods used are textual analysis and evaluation of concepts by means of historical comparison. The background to the study is given by the views of historians and sociologists according to whom traditional forms have ceased to exist and the market economy become established as the western system of values. The study identifies points of transition from the traditional forms to economic values. In addition, the dissertation focuses on the modern non-economic forms. The study examines the economic and ethical meanings of gift in antiquity in Homer, Plato, and Aristotle. Following Marcel Mauss, the study analyzes the forms and principles of gift exchange. The study also applies Nietzsche’s philosophy to evaluate under what conditions giving a gift becomes an act of exercising power that puts its receiver into debt. The conclusion of the study is that the classics of philosophy and sociology can rightly be interpreted in terms of the metaphysics of economy, but they also offer grounds for criticizing this metaphysics, even alternatives. One such alternative is non-economic archaic ethic. The study delineates a duality between economy and non-economy as well as creating concepts which could be used in the future to critically analyze economy from a position external to the economic system of concepts.

Naiset rajalla : Kyöpeli, Nainen, Naara(s), Neitsyt, Morsian, Akka ja Ämmä Suomen paikannimissä

Women at the boundary. Kyöpeli ( ghost, devil, elf, fairy, enchantress, witch ), Nainen ( woman ), Naara(s) ( female animal, derogatory term for a woman ), Neitsyt ( young, [virgin] woman ), Morsian ( bride ), Akka ( old woman, wife, grandmother ) and Ämmä ( [old] woman, wife, grandmother ) in Finnish place names This study examines a total of about 4,000 Finnish place names which include a specific that refers to a woman: Kyöpeli, Nainen, Naara(s), Neitsyt, Morsian, Akka or Ämmä. The study has two main objectives. First, to interpret the place names in the data, that is, to examine the words included in the data and establish their background and to differentiate names of different ages. In establishing the background of a name, the type of place (e.g. lake, hill or marsh) and its location, as well as the semantics of the feminine specific, are taken into account. The connotations of words referring to a woman are also studied. Words that refer to a woman are often affective and susceptible to changes in meaning, which is reflected in the history of place names. The second main objective is to recognise and highlight mythological place names. Mythology is pivotal for the interpretation of many place names with a feminine specific. The criteria for mythological names have not been explicitly discussed in Finnish onomastics until now, and I seek to determine such criteria in this study with the help of the data. Mythological place names often refer to large and significant natural localities, which are in many cases important boundaries for the community. Names for smaller localities may also be mythological if they refer to a place with a key location or a special topography (e.g. steep or rocky places). I also discuss the stories involved with specific places in the data, such as stories about supernatural beings. Each of the name groups discussed in the study has its own profile. For example, Naara(s) names are so old that naara is no longer understood to refer to a woman. These names have thus often been misinterpreted in onomastics. Names beginning with Morsian, on the other hand, appear to be of fairly recent origin and may be attributed to an international cautionary tale. Names beginning with Nais, Neitsyt, Akka and Ämmä highlight the duality of the data. They include both old names for important natural localities or boundaries and more recent names for modest dwellings, small cultivated areas and useless marshy ponds. This distribution of place names may reflect a cultural shift that changed the status of women in the community.

Conformal Field Theory Methods for Variants of Schramm-Loewner Evolutions

This thesis consists of an introduction, four research articles and an appendix. The thesis studies relations between two different approaches to continuum limit of models of two dimensional statistical mechanics at criticality. The approach of conformal field theory (CFT) could be thought of as the algebraic classification of some basic objects in these models. It has been succesfully used by physicists since 1980's. The other approach, Schramm-Loewner evolutions (SLEs), is a recently introduced set of mathematical methods to study random curves or interfaces occurring in the continuum limit of the models. The first and second included articles argue on basis of statistical mechanics what would be a plausible relation between SLEs and conformal field theory. The first article studies multiple SLEs, several random curves simultaneously in a domain. The proposed definition is compatible with a natural commutation requirement suggested by Dubédat. The curves of multiple SLE may form different topological configurations, ``pure geometries''. We conjecture a relation between the topological configurations and CFT concepts of conformal blocks and operator product expansions. Example applications of multiple SLEs include crossing probabilities for percolation and Ising model. The second article studies SLE variants that represent models with boundary conditions implemented by primary fields. The most well known of these, SLE(kappa, rho), is shown to be simple in terms of the Coulomb gas formalism of CFT. In the third article the space of local martingales for variants of SLE is shown to carry a representation of Virasoro algebra. Finding this structure is guided by the relation of SLEs and CFTs in general, but the result is established in a straightforward fashion. This article, too, emphasizes multiple SLEs and proposes a possible way of treating pure geometries in terms of Coulomb gas. The fourth article states results of applications of the Virasoro structure to the open questions of SLE reversibility and duality. Proofs of the stated results are provided in the appendix. The objective is an indirect computation of certain polynomial expected values. Provided that these expected values exist, in generic cases they are shown to possess the desired properties, thus giving support for both reversibility and duality.

On Random Planar Curves and Their Scaling Limits

Planar curves arise naturally as interfaces between two regions of the plane. An important part of statistical physics is the study of lattice models. This thesis is about the interfaces of 2D lattice models. The scaling limit is an infinite system limit which is taken by letting the lattice mesh decrease to zero. At criticality, the scaling limit of an interface is one of the SLE curves (Schramm-Loewner evolution), introduced by Oded Schramm. This family of random curves is parametrized by a real variable, which determines the universality class of the model. The first and the second paper of this thesis study properties of SLEs. They contain two different methods to study the whole SLE curve, which is, in fact, the most interesting object from the statistical physics point of view. These methods are applied to study two symmetries of SLE: reversibility and duality. The first paper uses an algebraic method and a representation of the Virasoro algebra to find common martingales to different processes, and that way, to confirm the symmetries for polynomial expected values of natural SLE data. In the second paper, a recursion is obtained for the same kind of expected values. The recursion is based on stationarity of the law of the whole SLE curve under a SLE induced flow. The third paper deals with one of the most central questions of the field and provides a framework of estimates for describing 2D scaling limits by SLE curves. In particular, it is shown that a weak estimate on the probability of an annulus crossing implies that a random curve arising from a statistical physics model will have scaling limits and those will be well-described by Loewner evolutions with random driving forces.

Conformal Field Theory Methods for Variants of Schramm-Loewner Evolutions

This thesis consists of an introduction, four research articles and an appendix. The thesis studies relations between two different approaches to continuum limit of models of two dimensional statistical mechanics at criticality. The approach of conformal field theory (CFT) could be thought of as the algebraic classification of some basic objects in these models. It has been succesfully used by physicists since 1980's. The other approach, Schramm-Loewner evolutions (SLEs), is a recently introduced set of mathematical methods to study random curves or interfaces occurring in the continuum limit of the models. The first and second included articles argue on basis of statistical mechanics what would be a plausible relation between SLEs and conformal field theory. The first article studies multiple SLEs, several random curves simultaneously in a domain. The proposed definition is compatible with a natural commutation requirement suggested by Dubédat. The curves of multiple SLE may form different topological configurations, ``pure geometries''. We conjecture a relation between the topological configurations and CFT concepts of conformal blocks and operator product expansions. Example applications of multiple SLEs include crossing probabilities for percolation and Ising model. The second article studies SLE variants that represent models with boundary conditions implemented by primary fields. The most well known of these, SLE(kappa, rho), is shown to be simple in terms of the Coulomb gas formalism of CFT. In the third article the space of local martingales for variants of SLE is shown to carry a representation of Virasoro algebra. Finding this structure is guided by the relation of SLEs and CFTs in general, but the result is established in a straightforward fashion. This article, too, emphasizes multiple SLEs and proposes a possible way of treating pure geometries in terms of Coulomb gas. The fourth article states results of applications of the Virasoro structure to the open questions of SLE reversibility and duality. Proofs of the stated results are provided in the appendix. The objective is an indirect computation of certain polynomial expected values. Provided that these expected values exist, in generic cases they are shown to possess the desired properties, thus giving support for both reversibility and duality.

AC transport at holographic quantum hall transitions

We compute AC electrical transport at quantum Hall critical points, as modeled by intersecting branes and gauge/gravity duality. We compare our results with a previous field theory computation by Sachdev, and find unexpectedly good agreement. We also give general results for DC Hall and longitudinal conductivities valid for a wide class of quantum Hall transitions, as well as (semi)analytical results for AC quantities in special limits. Our results exhibit a surprising degree of universality; for example, we find that the high frequency behavior, including subleading behavior, is identical for our entire class of theories.

Holographic Superfluids and Solitons

Superfluidity is perhaps one of the most remarkable observed macroscopic quantum effect. Superfluidity appears when a macroscopic number of particles occupies a single quantum state. Using modern experimental techniques one dark solitons) and vortices. There is a large literature on theoretical work studying the properties of such solitons using semiclassical methods. This thesis describes an alternative method for the study of superfluid solitons. The method used here is a holographic duality between a class of quantum field theories and gravitational theories. The classical limit of the gravitational system maps into a strong coupling limit of the quantum field theory. We use a holographic model of superfluidity to study solitons in these systems. One particularly appealing feature of this technique is that it allows us to take into account finite temperature effects in a large range of temperatures.