共查询到20条相似文献,搜索用时 725 毫秒
1.
Anton M. Zeitlin 《Communications in Mathematical Physics》2011,303(2):331-359
We define a quasiclassical limit of the Lian-Zuckerman homotopy BV algebra (quasiclassical LZ algebra) on the subcomplex,
corresponding to “light modes”, i.e. the elements of zero conformal weight, of the semi-infinite (BRST) cohomology complex
of the Virasoro algebra associated with vertex operator algebra (VOA) with a formal parameter. We also construct a certain
deformation of the BRST differential parametrized by a constant two-component tensor, such that it leads to the deformation
of the A
∞-subalgebra of the quasiclassical LZ algebra. Altogether this gives a functor the category of VOA with a formal parameter
to the category of A
∞-algebras. The associated generalized Maurer-Cartan equation gives the analogue of the Yang-Mills equation for a wide class
of VOAs. Applying this construction to an example of VOA generated by β - γ systems, we find a remarkable relation between the Courant algebroid and the homotopy algebra of the Yang-Mills theory. 相似文献
2.
We prove the decomposition theorem for the loop homotopy Lie algebra of quantum closed string field theory and use it to show that closed string field theory is unique up to gauge transformations on a given string background and given S-matrix. For the theory of open and closed strings we use results in open-closed homotopy algebra to show that the space of inequivalent open string field theories is isomorphic to the space of classical closed string backgrounds. As a further application of the open-closed homotopy algebra, we show that string field theory is background independent and locally unique in a very precise sense. Finally, we discuss topological string theory in the framework of homotopy algebras and find a generalized correspondence between closed strings and open string field theories. 相似文献
3.
We reformulate the algebraic structure of Zwiebach’s quantum open-closed string field theory in terms of homotopy algebras. We call it the quantum open-closed homotopy algebra (QOCHA) which is the generalization of the open-closed homotopy algebra (OCHA) of Kajiura and Stasheff. The homotopy formulation reveals new insights about deformations of open string field theory by closed string backgrounds. In particular, deformations by Maurer Cartan elements of the quantum closed homotopy algebra define consistent quantum open string field theories. 相似文献
4.
Eric?Harrelson Alexander?A.?Voronov J.?Javier?Zú?iga 《Letters in Mathematical Physics》2010,94(1):1-26
We set up a Batalin–Vilkovisky Quantum Master Equation (QME) for open-closed string theory and show that the corresponding
moduli spaces give rise to a solution, a generating function for their fundamental chains. The equation encodes the topological
structure of the compactification of the moduli space of bordered Riemann surfaces. The moduli spaces of bordered J-holomorphic curves are expected to satisfy the same equation, and from this viewpoint, our paper treats the case of the target
space equal to a point. We also introduce the notion of a symmetric Open-Closed Topological Conformal Field Theory (OC TCFT)
and study the L
∞ and A
∞ algebraic structures associated to it. 相似文献
5.
Alastair Hamilton 《Letters in Mathematical Physics》2009,89(2):115-130
In this paper we describe a construction which produces classes in compactifications of the moduli space of curves. This construction
extends a construction of Kontsevich which produces classes in the open moduli space from the initial data of a cyclic A
∞-algebra. The initial data for our construction are what we call a ‘quantum A
∞-algebra’, which arises as a type of deformation of a cyclic A
∞-algebra. The deformation theory for these structures is described explicitly. We construct a family of examples of quantum
A
∞-algebras which extend a family of cyclic A
∞-algebras, introduced by Kontsevich, which are known to produce all the kappa classes using his construction.
相似文献
6.
Christopher L. Rogers 《Letters in Mathematical Physics》2012,100(1):29-50
A manifold is multisymplectic, or more specifically n-plectic, if it is equipped with a closed nondegenerate differential form of degree n + 1. In previous work with Baez and Hoffnung, we described how the ‘higher analogs’ of the algebraic and geometric structures
found in symplectic geometry should naturally arise in 2-plectic geometry. In particular, just as a symplectic manifold gives
a Poisson algebra of functions, any 2-plectic manifold gives a Lie 2-algebra of 1-forms and functions. Lie n-algebras are examples of L
∞-algebras: graded vector spaces equipped with a collection of skew-symmetric multi-brackets that satisfy a generalized Jacobi
identity. Here, we generalize our previous result. Given an n-plectic manifold, we explicitly construct a corresponding Lie n-algebra on a complex consisting of differential forms whose multi-brackets are specified by the n-plectic structure. We also show that any n-plectic manifold gives rise to another kind of algebraic structure known as a differential graded Leibniz algebra. We conclude
by describing the similarities between these two structures within the context of an open problem in the theory of strongly
homotopy algebras. We also mention a possible connection with the work of Barnich, Fulp, Lada, and Stasheff on the Gelfand–Dickey–Dorfman
formalism. 相似文献
7.
Vasily Dolgushev 《Letters in Mathematical Physics》2011,97(2):109-149
We construct a 2-colored operad Ger
∞ which, on the one hand, extends the operad Ger
∞ governing homotopy Gerstenhaber algebras and, on the other hand, extends the 2-colored operad governing open-closed homotopy
algebras. We show that Tamarkin’s Ger
∞-structure on the Hochschild cochain complex C
•(A, A) of an A
∞-algebra A extends naturally to a Ger+¥{{\bf Ger}^+_{\infty}}-structure on the pair (C
•(A, A), A). We show that a formality quasi-isomorphism for the Hochschild cochains of the polynomial algebra can be obtained via transfer
of this Ger+¥{{\bf Ger}^+_{\infty}}-structure to the cohomology of the pair (C
•(A, A), A). We show that Ger+¥{{\bf Ger}^+_{\infty}} is a sub DG operad of the first sheet E
1(SC) of the homology spectral sequence for the Fulton–MacPherson version SC of Voronov’s Swiss Cheese operad. Finally, we
prove that the DG operads Ger+¥{{\bf Ger}^+_{\infty}} and E
1(SC) are non-formal. 相似文献
8.
We investigate the deformation of D-brane world-volumes in curved backgrounds. We calculate the leading corrections to the boundary conformal field theory involving
the background fields, and in particular we study the correlation functions of the resulting system. This allows us to obtain
the world-volume deformation, identifying the open string metric and the noncommutative deformation parameter. The picture
that unfolds is the following: when the gauge invariant combination ω=B+F is constant one obtains the standard Moyal deformation of the brane world-volume. Similarly, when dω= 0 one obtains the noncommutative Kontsevich deformation, physically corresponding to a curved brane in a flat background.
When the background is curved, H=dω≠ 0, we find that the relevant algebraic structure is still based on the Kontsevich expansion, which now defines a nonassociative
star product with an A
∞ homotopy associative algebraic structure. We then recover, within this formalism, some known results of Matrix theory in
curved backgrounds. In particular, we show how the effective action obtained in this framework describes, as expected, the
dielectric effect of D-branes. The polarized branes are interpreted as a soliton, associated to the condensation of the brane gauge field.
Received: 22 March 2001 / Accepted: 13 July 2001 相似文献
9.
We show that an algebra over a cyclic operad supplied with an additional linear algebra datum called Hodge decomposition admits a minimal model whose structure maps are given in terms of summation over trees. This minimal model is unique up to
homotopy.
J. Chuang is supported by an EPSRC advanced research fellowship. A. Lazarev is partially supported by an EPSRC research grant. 相似文献
10.
Florian Sch?tz 《Communications in Mathematical Physics》2009,286(2):399-443
We present a connection between the BFV-complex (abbreviation for Batalin-Fradkin-Vilkovisky complex) and the strong homotopy
Lie algebroid associated to a coisotropic submanifold of a Poisson manifold. We prove that the latter structure can be derived
from the BFV-complex by means of homotopy transfer along contractions. Consequently the BFV-complex and the strong homotopy
Lie algebroid structure are L
∞ quasi-isomorphic and control the same formal deformation problem.
However there is a gap between the non-formal information encoded in the BFV-complex and in the strong homotopy Lie algebroid
respectively. We prove that there is a one-to-one correspondence between coisotropic submanifolds given by graphs of sections
and equivalence classes of normalized Maurer-Cartan elemens of the BFV-complex. This does not hold if one uses the strong
homotopy Lie algebroid instead. 相似文献
11.
Martin Markl 《Communications in Mathematical Physics》2001,221(2):367-384
Barton Zwiebach constructed [20] “string products” on the Hilbert space of a combined conformal field theory of matter and
ghosts, satisfying the “main identity”. It has been well known that the “tree level” of the theory gives an example of a strongly
homotopy Lie algebra (though, as we will see later, this is not the whole truth).
Strongly homotopy Lie algebras are now well-understood objects. On the one hand, strongly homotopy Lie algebra is given by
a square zero coderivation on the cofree cocommutative connected coalgebra [13, 14]; on the other hand, strongly homotopy
Lie algebras are algebras over the cobar dual of the operad &?om for commutative algebras [9].
As far as we know, no such characterization of the structure of string products for arbitrary genera has been available, though
there are two series of papers directly pointing towards the requisite characterization.
As far as the characterization in terms of (co)derivations is concerned, we need the concept of higher order (co)derivations, which has been developed, for example, in[2, 3]. These higher order derivations were used in the analysis of the ”master
identity“. For our characterization we need to understand the behavior of these higher (co)derivations on (co)free (co)algebras.
The necessary machinery for the operadic approach is that of modular operads, anticipated in [5] and introduced in [8]. We believe that the modular operad structure on the compactified moduli space
of Riemann surfaces of arbitrary genera implies the existence of the structure we are interested in the same manner as was
explained for the tree level in [11].
We also indicate how to adapt the loop homotopy structure to the case of open string field theory [19].
Received: 10 November 1999 / Accepted: 29 March 2001 相似文献
12.
We show that infinite variety of Poincaré bialgebras with nontrivial classicalr-matrices generate nonsymmetric nonlinear composition laws for the fourmomenta. We also present the problem of lifting the
Poincaré bialgebras to quantum Poincaré groups by using e.g. Drinfeld twist, what permits to provide the nonlinear composition
law in any order of dimensionfull deformation parameterλ (from physical reasons we can putλ=λ
p whereλ
p is the Planck length). The second infinite variety of composition laws for fourmomentum is obtained by nonlinear change of
basis in Poincaré algebra, which can be performed for any choice of coalgebraic sector, with classical or quantum coproduct.
In last Section we propose some modification of Hopf algebra scheme with Casimir-dependent deformation parameter, which can
help to resolve the problem of consistent passage to macroscopic classical limit.
Presented at the 11th Colloquium “Quantum Groups and Integrable Systems”, Prague, 20–22 June 2002.
Supported by KBN grant 5PO3B05620 相似文献
13.
Hans-Werner Wiesbrock 《Communications in Mathematical Physics》1991,136(2):369-397
We give a rigorous definition of Witten'sC
*-string-algebra. To this end we present a new construction ofC
*-algebras associated to special geometric situations (Kähler foliations) and generalize this later construction to the string case. Through this we get a natural geometrical interpretation of the string of semi-infinite forms as well as the fermionic algebra structure. Using the (non-commutative) geometric concepts for investigating the string algebra we get a natural Fredholm module representation of dimension 26+.Work partially supported by the DFG (under contract MU 75712.3) 相似文献
14.
In this paper we construct a newN = 6 superconformal algebra which extends the Virasoro algebra by theSO
6 current algebra, by 6 odd primary fields of conformal weight 3/2 and by 10 odd primary fields of conformal weight 1/2. The
commutation relations of this algebra, which we will refer to asCK
6, are represented by short distance operator product expansions (OPE). We constructCK
6, as a subalgebra of theSO(6) superconformal algebra K6, thus giving it a natural representation as first order differential operators on the circle withN = 6 extended symmetry. We show thatCK
6 has no nontrivial central extensions.
Partially supported by NSC grant 85-2121-M-006-019 of the ROC.
Partially supported by NSF grant DMS-9622870. 相似文献
15.
Alexander Astashkevich Alexander Belopolsky 《Communications in Mathematical Physics》1997,186(1):109-136
We consider the theory of bosonic closed strings on the flat background ℝ25,1. We show how the BRST complex can be extended to a complex where the string center of mass operator,x
0
μ
is well defined. We investigate the cohomology of the extended complex. We demonstrate that this cohomology has a number
of interesting features. Unlike in the standard BRST cohomology, there is no doubling of physical states in the extended complex.
The cohomology of the extended complex is more physical in a number of aspects related to the zero-momentum states. In particular,
we show that the ghost number one zero-momentum cohomology states are in one to one correspondence with the generators of
the global symmetries of the backgroundi.e., the Poincaré algebra.
Supported in part by funds provided by the U.S. Department of Energy (D.O.E.) under cooperative agreement #DF-FC02-94ER40818 相似文献
16.
Olga Kravchenko 《Letters in Mathematical Physics》2007,81(1):19-40
Structures of Lie algebras, Lie coalgebras, Lie bialgebras and Lie quasibialgebras are presented as solutions of Maurer–Cartan
equations on corresponding governing differential graded Lie algebras using the big bracket construction of Kosmann–Schwarzbach.
This approach provides a definition of an L
∞-(quasi)bialgebra (strongly homotopy Lie (quasi)bialgebra). We recover an L
∞-algebra structure as a particular case of our construction. The formal geometry interpretation leads to a definition of an
L
∞ (quasi)bialgebra structure on V as a differential operator Q on V, self-commuting with respect to the big bracket. Finally, we establish an L
∞-version of a Manin (quasi) triple and get a correspondence theorem with L
∞-(quasi)bialgebras.
This paper is dedicated to Jean-Louis Loday on the occasion of his 60th birthday with admiration and gratitude. 相似文献
17.
T. V. Dudnikova 《Russian Journal of Mathematical Physics》2006,13(2):123-130
We consider the dynamics of a harmonic crystal in n dimensions with d components, where d and n are arbitrary, d, n ⩾ 1. The initial data are given by a random function with finite mean energy density which also satisfies a Rosenblatt-or
Ibragimov-type mixing condition. The random function is close to diverse space-homogeneous processes as x
n
→ ±∞, with the distributions μ±. We prove that the phase flow is mixing with respect to the limit measure of statistical
solutions.
Partially supported by RFBR under grant no. 06-01-00096. 相似文献
18.
F. Finster N. Kamran J. Smoller S.-T. Yau 《Communications in Mathematical Physics》2006,264(2):465-503
We consider the Cauchy problem for the massless scalar wave equation in the Kerr geometry for smooth initial data compactly
supported outside the event horizon. We prove that the solutions decay in time in L
∞
loc. The proof is based on a representation of the solution as an infinite sum over the angular momentum modes, each of which
is an integral of the energy variable ω on the real line. This integral representation involves solutions of the radial and angular ODEs which arise in the separation
of variables.
Research supported in part by the Deutsche Forschungsgemeinschaft.
Research supported by NSERC grant #RGPIN 105490-2004.
Research supported in part by the NSF, Grant No. DMS-010-3998.
Research supported in part by the NSF, Grant No. 33-585-7510-2-30.
An erratum to this article is available at . 相似文献
19.
H. Amirhashchi H. Zainuddin Anirudh Pradhan 《International Journal of Theoretical Physics》2011,50(8):2531-2545
Exact solution of Einstein’s field equations is obtained for massive string cosmological model of Bianchi III space-time using
the technique given by Letelier (Phys. Rev. D 28:2414, 1983) in presence of perfect fluid and decaying vacuum energy density Λ. To get the deterministic solution of the field equations
the expansion θ in the model is considered as proportional to the eigen value s2 2\sigma^{2}_{~2} of the shear tensor sj i\sigma^{j}_{~i} and also the fluid obeys the barotropic equation of state. It is observed that the particle density and the tension density
of the string are comparable at the two ends and they fall off asymptotically at similar rate. But in early stage as well
as at the late time of the evolution of the universe we have two types of scenario (i) universe is dominated by massive strings
and (ii) universe is dominated by strings depending on the nature of the two constants L and ℓ. The value of cosmological constant Λ for the model is found to be small and positive which is supported by the results from
recent supernovae Ia observations. Some physical and geometric properties of the model are also discussed. 相似文献
20.
K. A. Bronnikov B. E. Meierovich 《Journal of Experimental and Theoretical Physics》2008,106(2):247-264
We consider (d
0 + 2)-dimensional configurations with global strings in two extra dimensions and a flat metric in d
0 dimensions, endowed with a warp factor e
2γ depending on the distance l from the string center. All possible regular solutions of the field equations are classified by the behavior of the warp
factor and the extradimensional circular radius r(l). Solutions with r → ∞ and r → const > 0 as l → ∞ are interpreted in terms of thick brane-world models. Solutions with r → 0 as l → l
c > 0, i.e., those with a second center, are interpreted as either multibrane systems (which are appropriate for large enough
distances l
c between the centers) or as Kaluza-Klein-type configurations with extra dimensions invisible due to their smallness. In the
case of the Mexican-hat symmetry-breaking potential, we build the full map of regular solutions on the (ɛ, Γ) parameter plane,
where ɛ acts as an effective cosmological constant and Γ characterizes the gravitational field strength. The trapping properties
of candidate brane worlds for test scalar fields are discussed. Good trapping properties for massive fields are found for
models with increasing warp factors. Kaluza-Klein-type models are shown to have nontrivial warp factor behaviors, leading
to matter particle mass spectra that seem promising from the standpoint of hierarchy problems.
The text was submitted by the authors in English. 相似文献