Our starting point is the notion that the string field coordinates x. For the bosonic string this is due to zwiebach 92, equation 4. Background independent action for double field theory. We propose classical string field solutions relating any two toroidal backgrounds and discuss the space.
For a given cy3, a nonperturbative defintion of topological string theory can be given in terms of the gauge theory on branes wrapping cycles of the cy3. March 2327, 2009 stony brook university string field theory has been an active area of research for the past several years. If we consider the string field as an infinite sum of classical fields, can. This is accomplished at the level of perturbation theory by finding a collection of vertices for joining and splitting strings, as well as string propagators, that give a feynman diagramlike expansion for string scattering amplitudes. String theory was once the hottest thing in physics. The brst operator that defines the quadratic kinetic term of string field theory may be regarded as the solution of the equation of motion aa0 of a purely cubic background independent string field theory. Quantum field theory ii introductions to quantum gravity. In the 1980s and 90s, it promised seemingly unlimited bounty. String theory, ot its modern incarnation mtheory, gives a huge. With the method of erler and maccaferri, it is now possible to study.
This is achieved through the definition of an extended spacetime that geometrises the tduality group od,d in dft and exceptional uduality groups in eft. Arising from the notion that matter and energy are fundamentally composed of tiny, vibrating strings rather than pointlike particles, this theory attempted to unify all the known forces into a single, elegant package. In this thesis, recent developments in double field theory dft and exceptional field theory eft are presented. Perhaps a better understanding of the topological m theory in 7 dimensions will help. Edward witten, on background independent open string field theory, phys.
Double field theory describes a massless subsector of closed string theory with both momentum and winding excitations. It has been shown recently that the background independent open string field theory provides an exact description of the tachyon condensation on unstable dbranes of bosonic string theory. All of the tools and concepts that are needed to quantize strings are developed first for point particles. Simons center for geometry and physics workshop on string. For example, matrix string theory is a nonperturbative definition of type iia string theory and it exactly defines the theory for any finite value of g but its still backgrounddependent because you cant use the theory for backgrounds with additional dimensions compactified on a calabiyau, and most other similar things.
The new star product is formulated in a halfphasespace, and because phase space is independent of any background. Themathematicsofmtheory robbert dijkgraaf abstract. In this basis there is a large amount of symmetry, including a supersymmetry ospd2 that acts on matter and ghost. Background independenc oe f string field theory ashoke sen tata institute fundamental of research, homi bhabha road, bombay 400005, india abstract we formulate closed string field theories in background described by arbitrary two dimensional conformally invariant field theories, study the classical equations of motion in these theories, and. Quantum loop theory pdf an elementary introduction to quantum gravity and spinfoam theory. String theory is a backgrounddependent theory built on a fixed framework, so it doesnt currently account for the dynamic nature of spacetime at the heart of relativity. I had the impossible task of beginning with some basic formal structure of mechanics and ending with su.
Background independent algebraic structures in closed string field theory ashoke sen and barton zwiebach. We construct a batalinvilkovisky bv algebra on moduli spaces of riemann surfaces. Normalization of the background independent open string. Beckerbeckerschwarz try to jump to the truly consistent full theory, which is the supersymmetric one, as quickly as they can so the general bosonic string theorys effective action may be absent in the book. In physics, string theory is a theoretical framework in which the pointlike particles of particle physics are replaced by onedimensional objects called strings. Pdf background independent string field theory dmitry. Simons center for geometry and physics workshop on string field theory 2009. Freed introduction these notes are expanded versions of seven lectures given at the iaspark city mathematics institute. The fall and rise of string theory discover magazine. In this analysis the overall normalisation of the action was chosen so that it reproduces the conjectured relations involving tachyon condensation.
Quantum field theory of point particles and strings. Background independent open string field theory with. Background independent open string field theory with constant bfield on the annulus r. Pdf exact renormalization group and loop variables. A framework for backgroundindependent openstring field theory is proposed. We develop a new background independent moyal star formalism in bosonic open string field theory. Introduction to quantum field theory were the most di. The purpose of this book is to introduce string theory without assuming any background in quantum field theory. String field theory is a nonperturbative approach to string theory which holds some promise towards providing a backgroundindependent definition of the theory.
They are reformulation of supergravity in which duality symmetries are made manifest before dimensional reduction. The approach involves using the batalinvilkovisky formalism. Some aspects of eld theory are popular in algebra courses at the undergraduate or graduate levels, especially the theory of nite eld extensions and galois theory. The new star product is formulated in a halfphasespace, and because phase space is independent of any background fields, the interactions are. We show that in the large noncommutativity limit the action of tachyon field is given exactly by the potential term which has the same form as in the case without bfield but the product of. Additionally it was shown in 62 that this v acuum is background independent exactly due to the. Since the discovery of the tachyon vacuum solution, the classical solutions of cubic string field theory have been studied quite actively 321. We construct the associated nonlinear backgroundindependent action that is tduality invariant and realizes the courant gauge algebra. At present it seems that these three independent ideas are closely related, and perhaps essentially equivalent. This book is an introduction to loop quantum gravity lqg focusing on its co. On backgroundindependent openstring field theory request pdf. Conformal theories define a homomorphism of this algebra to the bv algebra of string functionals.
But the corresponding action for the superstring theory is on page 311 etc. If string field theory is string theory reformulated in the language of quantum field theory, and qft is background dependent, how does the background independence in sft arise. String field theory sft is a formalism in string theory in which the dynamics of relativistic strings is reformulated in the language of quantum field theory. In addition, the different spacetime configurations should be obtained as different solutions of the underlying equations. Electromagnetic field theory a problemsolving approach.
Background fields in string theory physics stack exchange. Background independent algebraic structures in closed. In another sense, sft is no more or no less background independant or dependant than regular string theory, bc it essentially just reproduces perturbation series and might miss some but not all of the nonperturbative backgrounds that also must exist in a full theory. Theory with gravity is dual to theory without gravity like gauge symmetry, general covariance is a derived concept precise definition of string theory as least in negatively curved spacetime new insights into gauge theory and string theory, in particular, holography and issues in the black hole information puzzle. On distance scales larger than the string scale, a string looks just like an ordinary particle, with its mass, charge, and other properties. According to the lqg researchers, a theory of quantum gravity must be backgroundindependent, a theory that explains space and time instead of being plugged into an. Quantum gravity theory pdf 2 how to search for quantum gravity. Pdf on background independence in string theory researchgate. Theres also string field theory, which is fully background independent, but progress in it is slow and interest in it has declined exponentially since the early 1990s. Cubic string field theory in ppwave background and background independent moyal structure. Pdf cubic string field theory in ppwave background and. String theory relies on supersymmetry to keep it from requiring an obscenely high number of dimensions in order for it to work. Background independence is a condition in theoretical physics, that requires the defining equations of a theory to be independent of the actual shape of the spacetime and the value of various fields within the spacetime. The construction begins with a gradedcommutative free associative algebrac built from.
There have been important technical advances, especially in the construction of classical solutions of open string field theory. Recent work using wittens cubic open string field theory. On the background independence of string field theory. The book qualifies as a very valuable addition to the quantum field theory literature with the distinctive merit of presenting quantum gravity, supersymmetry and string theory in a clear way accessible to graduate students and likely useful also to researchers in quantum field theory and elementary particle theory. Lectures on dbranes, tachyon condensation, and string field theory. Yangz department of physics simon fraser university vancouver, bc v5a 1s6 canada abstract we study wittens background independent open string eld theory in the presence of a constant b eld at one loop level. Target space duality as a symmetry of string field theory. The new star product is formulated in a halfphasespace, and because phase space is independent of any background fields, the interactions are background independent. Request pdf a framework for background independent openstring field theory is proposed. In a recent paper, erler and maccaferri have given a way to realize any boundary conformal field theory bcft as a solution of the equation of motion. Be aware there are several versions of string field theory. What is background independence and how important is it in order to be a theory of everything, will the final stringtheorymtheory have to be background independent. In this paper we fix this normalisation by comparing the on. The application to string theory was explained by friedan, martinec and shenker in conformal invariance, supersymmetry and string theory, nucl.
The construction begins with a gradedcommutative free associative algebra c built from the vector. Does the current lack of background independence show string theory is currently not a theory of everything my understanding from wikipedia is that the adscft shows hopeful hints. The gauge algebra is governed by the courant bracket in certain subsectors of this double field theory. It describes how these strings propagate through space and interact with each other. This algebra is background independent in that it makes no reference to a state space of a conformal field theory. String field theory solution corresponding to constant. Pdf exceptional field theory and supergravity semantic. In particular this means that it must be possible not to refer to a specific coordinate systemthe theory must be coordinatefree. Field theory 3 about these notes the purpose of these notes is to give a treatment of the theory of elds. Its lowest excitations are the modes that correspond to.
There is now a standard reference on relativistic string theory by. Part i of this book follows the development of quantum field theory for point particles, while part ii introduces strings. Background independent open string field theory core. A background independent approach to string theory article pdf available in international journal of modern physics a 3032 august 2015 with. A framework for background independent openstring field theory is proposed. We analyze the tachyon field in the bosonic open string theory in a constant bfield background using the background independent open string field theory.
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