We extend the bfss matrix theory by means of lie 3algebra. We use fx to represent the set of all polynomials of x with coe cients in f. By treating appropriate configurations as backgrounds, we derive the bfss matrix theory and the iib. In physics, matrix string theory is a set of equations that describe superstring theory in a nonperturbative framework. Applied matrix theory j lecture notes for math 464514 presented by dr. The bfss matrix theory is conjectured to describe infinite momentum frame imf limit of m theory in 2 and many evidences were found. The goal of the present paper is to formulate the ikkt and bfss matrix models. With a few changes, the same formalism can handle much more complicated situations. Threealgebra bfss matrix theory harvard university. For a various matrix size n respecting the t hooft scaling, we find quantitative evidence for the formation of a single bound state of d0branes at late time, which is matrix model thermalization and dual to the formation of a larger black hole. From those terms, they read o the coupling of dbranes to weak background elds, and fur. On supersymmetry of the covariant 3algebra model for m.
The name matroid suggests a structure related to a matrix and, indeed, matroids were introduced by whitney 61 in 1935 to provide a unifying abstract treatment of dependence in linear algebra and graph theory. In the large n limit of a large number of d0branes this is supposed to encode the strong coupling limit of type iia string theory known as mtheory. As a consequence, our simulations correspond to the ungauged version of the bfss or bosonic matrix models, where no. In mathematics, a matrix is a rectangular array of numbers or other data. It is clear that the characteristic polynomial is an nth degree polynomial in. Chapter 5 theory of matrices as before, f is a eld. These calculations led them to propose that the bfss matrix model is exactly equivalent to m theory. We study dynamics of the model by choosing the minimal lie 3. Hermann nicolai, robert helling, supermembranes and matrix theory, lectures given by h. Threealgebra bfss matrix theory international journal. To be specific, these dualities can be portrayed on a map as you can see in the image here. The paper includes an introduction for mathematicians to the ikkt formulation of matrix theory and its relation to the bfss matrix theory. The argument that the regularized m2brane worldvolume theory is the bfss matrix model is discussed in.
Matrix theory relies on the adscft correspondence, specifically, that. E ective action of matrix theory 10 gives insight for the multiple dbrane action. But the two most influential suggestions were the comprehensive sociological versions of systems theory. In particular he has made an important contribution to the conjectured banksfishlershenkersusskind bfss matrix model of string theory and m theory.
A simple vev should lead to the generation of the bfss matrix model, including other backgrounds such as matrix string theory, he argues. Bfss matrix theory and iib matrix model from covariant 3algebra model for m theory. Chapter 2 contains a lightning introduction into string theory and some other related topics. The extended model possesses the same supersymmetry as the original bfss matrix theory, and thus as the infinite momentum frame limit of. Most textbooks dont cover it, or only cover it very superficially. Bfss matrix model 2 is the maximally supersymmetric matrix quantum. We consider the scattering of a single particle from a. Precisely, the action of berkoozdouglas bd matrix theory is the 00 and 04 string sectors of the sym describing the d0d4 bound state, which is given by the dimensional reduction of the d6, n 1 sym. We apply this idea to matrix quantum mechanics, which is relevant, for instance, to nonperturbative studies of the bfss matrix theory, a conjectured nonperturbative definition of m theory. M theory is basically a stronglycoupled theory in 11 dimensions from which other string theories can be derived from. The bfss matrix model banksfischlershenkersusskind 96, seiberg 97 is the description of the worldline dynamics of interacting d0branes. Chapter 3 deals mostly with the bfss matrix quantum mechanics but also with the dvv matrix gauge theory and their physics.
Random matrix theory is now a big subject with applications in many disciplines of science, engineering and. I will have to check whether it makes sense because similar methods to make the bfss matrix model timeless have been tried in the past and none of them looked manifestly lorentzcovariant, if i remember well. Henceforth, we consider only the bosonic part of the lagrangian of. In the second superstring revolution, it was realised that the ordinary 5 string theoryies were connected by 2 dualities, namely tduality and sduality. We identify the supersymmetric ground state of this hamiltonian with the tachyonic vacuum. In this paper, we concentrate on the classical dynamics, and set fermion to zero for simplicity. The bfss model is closely related to another basic model often known as the ikkt matrix theory 2 and obtained by reduction of 10d sym theory to a point 3. Type iia string theory can be shown to be equivalent to a maximally supersymmetric twodimensional gauge theory, the gauge group of which is u for a large value of n. Since bfss matrix model is dual to the higher dimensional spacetime, it would be very interesting. The evidence for the conjecture consists of several correspondences between the two theories. Quantum black hole formation in the bfss matrix model. I attempt to give a pedagogical introduction to the matrix model of m theory as developed by banks, fischler, shenker and susskind bfss. On emergent geometry from entanglement entropy in matrix. It is known that for generic initial conditions, the bmn matrix model is.
Bfss matrix theory, also known as matrix theory is a fully nonpeturbative. In practice however, the latter provides for a more precise dictionary between a gauge theory and string theory, while computations in the bfss and bmn matrix theories quickly become 4. The two models, known as the bfss matrix model and the ikkt matrix model, are closely related. These m theory inspired matrix models can also be related to the adscft or gravitational holography conjecture 29, 30. The bfss matrix model can therefore be used as a prototype for a correct formulation of m theory and a tool for investigating the properties of m theory in a relatively simple setting. The bfss matrix theory and the iib matrix model 35 can be obtained by the matrix regularization of the poisson brackets of the lightcone membrane theory 36 and of greenschwarz string theory in schild gauge 35, respectively.
The extended model possesses the same supersymmetry as the original bfss matrix theory, and thus as the infinite momentum frame limit of m theory. But ive heard that matrix string theory does both a nonpeturbative formulation of type iia string theory and a nonpeturbative type he string theory. Theory, type iib matrix model and matrix string theory arxiv. We suggest and motivate a precise equivalence between uncompactified eleven dimensional mtheory and the n infinity limit of the supersymmetric matrix quantum mechanics describing d0branes. A matrix model describes the behavior of a set of matrices within the framework of. Nicolai at the trieste spring school on nonperturbative aspects of string theory and supersymmetric gauge theories, 23 31 march 1998 arxiv. Bfss matrix theory mathematics and physics wiki fandom. From the model, we derive the bfss matrix theory and the iib matrix model in a large n limit by taking appropriate vacua. Explain the general method for solving simultaneous equations. What is the basic idea behind matrix string theory.
While the bfss conjecture was originally formulated in the large nregime, the bfss matrix theory at nite nis believed to describe discrete lightcone quantized dlcq mtheory 22,24. The extended model possesses the same supersymmetry as the. Feb 08, 2009 a simple vev should lead to the generation of the bfss matrix model, including other backgrounds such as matrix string theory, he argues. Furthermore, in the same way that the euclidean ikkt matrix model decompactified on a circle s 1 gives the bfss model at finite temperature, matrix theory decompactified on a circle s 1 should give the above dvv matrix string theory. A good start with defining mtheory was given by the matrix theory approach of. Pdf black hole and fuzzy objects in bfss matrix model.
On emergent geometry from entanglement entropy in matrix theory. Threealgebra bfss matrix theory international journal of. The two models, known as the bfss matrix model and the ikkt. Pdf we analyze fuzzy configurations of d0branes in bfss matrix model as.
Where can i find a good introductory text for matrix string theory. String theory describes how strings propagate through space and interact with each other. Then detai is called the characteristic polynomial of a. Bfss matrix theory is an example of a matrix model. Supersymmetric action of multiple d0branes from matrix theory. In the large n limit of a large number of d0branes this is supposed to encode the strong coupling limit of type iia string theory known as m theory at least in certain corners of its moduli space the bfss model is a limiting case of the bmn. The entire analysis is carried out using the known hamiltonian of the matrix model, which is equivalent to the hamiltonian of the nc gauge theory.
It is a matrix model for type iia string theory and type he string theory. Introduction to string theory mathematics and physics. The individual values in the matrix are called entries. Good introductory text for matrix string theory stack exchange. Spherical m5branes from the plane wave matrix model. More generally, matrix quantum mechanics provides a rather generic system for studying quantum chaos 68. Masanori hanada, what lattice theorists can do for superstringm theory, international journal of modern physics avol.
As a consequence of supersymmetry the simple matrix model is rich enough to describe the properties of. Because the regularization replaces a two dimensional integral over a world volume by a trace. Matrix theory prop osal of banks, fisc hler, shenk er and susskind bfss 3 mtheory in the in. We examine a natural supersymmetric extension of the bosonic covariant 3algebra model for m theory proposed in 1. The bfss matrix model is also considered the worldvolume theory of a large number of d0branes in type iia string theory remember the rst slide. Pdf quantum black hole formation in the bfss matrix model. As a consequence, our simulations correspond to the ungauged version of the bfss or bosonic matrix models, where no gauge constraints are imposed on the state vectors. The partition functions of the dvv, bfss and ikkt matrix models 1. Matrix model, noncommutative gauge theory and the tachyon. Witten index of minibfss vanishes at any n, and while we have only given evidence for.
The covariant 3algebra model for m theory possesses a large moduli that includes simultaneously diagonalizable configurations. In the heuristic derivation given by sen and seiberg, 14, this lightlike compacti. On supersymmetry of the covariant 3algebra model for mtheory. So, is bfss matrix theory a type of matrix string theory. In physics, a matrix model is a particular kind of physical theory whose mathematical formulation involves the notion of a matrix in an important way. Mar 18, 2015 pdf we study the various headon collisions of two bunches of d0branes and their realtime evolution in the bfss matrix model in classical limit. Sens conjecture about the latter follows simply from this identification. Compared to the original bfss matrix theory, this theory has extra degrees of freedom, and has only half of the supersymmetries. As a consequence of supersymmetry the simple matrix model is rich enough to describe the properties of the. The starting point for string theory is the idea that the pointlike particles of particle physics can also be modeled as onedimensional objects called strings. It gives us a fully nonperturbative formulation of m theory, but only in antidesitter space. String theory is a proposed perturbative theory that would unify all of the fundamental forces of physics. The bfss matrix model is also considered the worldvolume theory of a large number of d0branes in type iia string theory.
In particular the continuum version of the quenched eguchikawai model may be useful in studying supersymmetric andor chiral gauge theories nonperturbatively. Systems theory international encyclopedia of political science. In the context of bfss model, one of the limitations of the gaussian state approximation is that the gauge symmetry constraints cannot be fully respected. Jhep0820154 bmn matrix model corresponds to a classical solution of the n 1eld theory see 6 and references therein. While the bfss conjecture was originally formulated in the large nregime, the bfss matrix theory at nite nis believed to describe discrete lightcone quantized dlcq m theory 22,24. The spectrum is a continuum, corresponding to the degree of freedom of bubbling o. String theory is a theoretical framework that attempts to address these questions and many others. We suggest and motivate a precise equivalence between uncompactified eleven dimensional m theory and the n infinity limit of the supersymmetric matrix quantum mechanics describing d0branes. One such proposal is the bfss model 1 3 which was conjectured to capture the entire dynamics of m theory 1. Nonabelian action of d0branes from matrix theory in the. Second prove that any permutation matrix is a product of such matrices. Mathematics for engineers basic matrix theory tutorial 2 this is the second of two tutorials on matrix theory.
On completion you should be able to do the following. Pdf we study the various headon collisions of two bunches of d0branes and their realtime evolution in the bfss matrix model in classical limit. The bfss model can be obtained as a the regularized and quantized 11 dimensional supermembrane theory, or as b the discrete lightcone quantization dlcq of mtheory. The bfss matrix theory of 8 is based on a discrete ligh t cone qu an tizat ion dlcq of m theory. Bfss matrix model 2 is the maximally supersymmetric matrix quantum mechanics, which is the dimensional reduction of 4d n 4 supersymmetric yangmills theory to one dimension time. Third prove that invertible diagonal matrix with a single element di erent from 1 is an elementary matrix. We study the various headon collisions of two bunches of d0branes and their realtime evolution in the bfss matrix model in classical limit. In the large n limit of a large number of d0branes this is supposed to encode the strong coupling limit of type iia string theory known as m theory at least in certain corners of its moduli space. The bfss matrix model banksfischlershenkersusskind 96, seiberg 97. It was proposed by banks, fischler, shenker, and susskind in 1996. In theoretical physics, the bfss matrix model or matrix theory is a quantum mechanical model. In the heuristic derivation given by sen and seiberg, 14, this light.
Prove that any invertible diagonal matrix is a product of such matrices and apply exercise 2. In the context of string theory we mean by m atrix theory the bfss matrix quantum mechanics and its bmn ppwave deformation. Taylor and van raamsdonk studied the e ective action of bfss matrix theory in detail and found the terms which can be interpreted as the supergravity interactions. Relation to string theory m theory such as via bfss matrix model in view adscft duality. Along with willy fischler, stephen shenker, and leonard susskind, he is one of the four originators of matrix theory, or bfss matrix theory, an attempt to formulate m theory in a nonperturbative manner. Bfss matrix theory, also known as matrix theory is a fully nonpeturbative formulation of m theory.
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