共查询到20条相似文献,搜索用时 24 毫秒
1.
Krzysztof Gawȩdzki Rafał R. Suszek Konrad Waldorf 《Communications in Mathematical Physics》2008,284(1):1-49
The simplest orientifolds of the WZW models are obtained by gauging a symmetry group generated by a combined involution of the target Lie group G and of the worldsheet. The action of the involution on the target is by a twisted inversion , where ζ is an element of the center of G. It reverses the sign of the Kalb-Ramond torsion field H given by a bi-invariant closed 3-form on G. The action on the worldsheet reverses its orientation. An unambiguous definition of Feynman amplitudes of the orientifold
theory requires a choice of a gerbe with curvature H on the target group G, together with a so-called Jandl structure introduced in [31]. More generally, one may gauge orientifold symmetry groups
that combine the -action described above with the target symmetry induced by a subgroup Z of the center of G. To define the orientifold theory in such a situation, one needs a gerbe on G with a Z-equivariant Jandl structure. We reduce the study of the existence of such structures and of their inequivalent choices to
a problem in group-Γ cohomology that we solve for all simple simply connected compact Lie groups G and all orientifold groups .
Membre du C.N.R.S. 相似文献
2.
Marek Biskup Lincoln Chayes Shannon Starr 《Communications in Mathematical Physics》2007,269(3):611-657
We develop a novel approach to phase transitions in quantum spin models based on a relation to their classical counterparts. Explicitly, we show that whenever chessboard estimates can be used to prove a phase transition in the classical model, the corresponding quantum model will have a similar phase transition, provided the inverse temperature β and the magnitude of the quantum spins satisfy . From the quantum system we require that it is reflection positive and that it has a meaningful classical limit; the core technical estimate may be described as an extension of the Berezin-Lieb inequalities down to the level of matrix elements. The general theory is applied to prove phase transitions in various quantum spin systems with . The most notable examples are the quantum orbital-compass model on and the quantum 120-degree model on which are shown to exhibit symmetry breaking at low-temperatures despite the infinite degeneracy of their (classical) ground state. 相似文献
3.
Orlin Stoytchev 《Letters in Mathematical Physics》2007,79(3):235-249
Any -graded C
*-dynamical system with a self-adjoint graded-Kubo-Martin-Schwinger (KMS) functional on it can be represented (canonically)
as a -graded algebra of bounded operators on a -graded Hilbert space, so that the grading of the latter is compatible with the functional. The modular conjugation operator
plays a crucial role in this reconstruction. The results are generalized to the case of an unbounded graded-KMS functional
having as dense domain the union of a net of C
*-subalgebras. It is shown that the modulus of such an unbounded graded-KMS functional is KMS.
相似文献
4.
Roderich Tumulka 《Letters in Mathematical Physics》2008,84(1):41-46
We prove a theorem about positive-operator-valued measures (POVMs) that is an analog of the Kolmogorov extension theorem,
a standard theorem of probability theory. According to our theorem, if a sequence of POVMs G
n
on satisfies the consistency (or projectivity) condition then there is a POVM G on the space of infinite sequences that has G
n
as its marginal for the first n entries of the sequence. We also describe an application in quantum theory.
The main proof in this article was first formulated in my habilitation thesis [6]. 相似文献
5.
S. Majid 《Czechoslovak Journal of Physics》1997,47(1):79-90
We obtain new family of quasitriangular Hopf algebras
via the author's recent double-bosonisation construction for new quantum groups. They are versions of U
q(su
n+1) with a fermionic rather than bosonic quantum plane of roots adjoined to U
q(su
n). We give the n = 2 case in detail. We also consider the anyonic-double of an anyonic (
) braided group and the double-bosonisation of the free braided group in n variables. 相似文献
6.
We show that the affine quantum group
is isomorphic to a bicross-product central extension
of the quantum loop group
by a quantum cocycle
in R-matrix form. 相似文献
7.
Local Asymptotic Normality in Quantum Statistics 总被引:1,自引:1,他引:0
The theory of local asymptotic normality for quantum statistical experiments is developed in the spirit of the classical result
from mathematical statistics due to Le Cam. Roughly speaking, local asymptotic normality means that the family consisting of joint states of n identically prepared quantum systems approaches in a statistical sense a family of Gaussian state ϕ
u
of an algebra of canonical commutation relations. The convergence holds for all “local parameters” such that parametrizes a neighborhood of a fixed point .
In order to prove the result we define weak and strong convergence of quantum statistical experiments which extend to the
asymptotic framework the notion of quantum sufficiency introduces by Petz. Along the way we introduce the concept of canonical
state of a statistical experiment, and investigate the relation between the two notions of convergence. For the reader’s convenience
and completeness we review the relevant results of the classical as well as the quantum theory.
Dedicated to Slava Belavkin on the occasion of his 60th anniversary 相似文献
8.
Reiji Tomatsu 《Communications in Mathematical Physics》2007,275(1):271-296
Let be a co-amenable compact quantum group. We show that a right coideal of is of quotient type if and only if it is the range of a conditional expectation preserving the Haar state and is globally
invariant under the left action of the dual discrete quantum group. We apply this result to the theory of Poisson boundaries
introduced by Izumi for discrete quantum groups and generalize a work of Izumi-Neshveyev-Tuset on SU
q
(N) for co-amenable compact quantum groups with the commutative fusion rules. More precisely, we prove that the Poisson integral
is an isomorphism between the Poisson boundary and the right coideal of quotient type by a maximal quantum subgroup of Kac
type. In particular, the Poisson boundary and the quantum flag manifold are isomorphic for any q-deformed classical compact Lie group. 相似文献
9.
The notion of a p-adic superspace is introduced and used to give a transparent construction of the Frobenius map on p-adic cohomology of a smooth projective variety over (the ring of p-adic integers), as well as an alternative construction of the crystalline cohomology of a smooth projective variety over
(finite field with p elements).
Partly supported by NSF grant No. DMS 0505735. 相似文献
10.
Clifford H. Taubes 《Communications in Mathematical Physics》2006,267(1):25-64
I describe a functional integral for maps from
to a Lie group or its quotient which has a simple renormalization that leads to a quantum field theory for maps from
into the Lie group or its quotient whose Hamiltonian is the time translation generator for a unitary action of the n+1 dimensional Poincaré group on the quantum Hilbert space. I also explain how the renormalization provides a functional integral for maps from a Riemann surface to a compact Lie group or its quotient that exhibits many conformal field theoretic properties.Support in part by a grant from the National Science Foundation 相似文献
11.
Markus Heydenreich Remco van der Hofstad 《Communications in Mathematical Physics》2007,270(2):335-358
We investigate the scaling of the largest critical percolation cluster on a large d-dimensional torus, for nearest-neighbor percolation in sufficiently high dimensions, or when d > 6 for sufficiently spread-out percolation. We use a relatively simple coupling argument to show that this largest critical
cluster is, with high probability, bounded above by a large constant times V
2/3 and below by a small constant times , where V is the volume of the torus. We also give a simple criterion in terms of the subcritical percolation two-point function on
under which the lower bound can be improved to small constant times , i.e. we prove random graph asymptotics for the largest critical cluster on the high-dimensional torus. This establishes a conjecture by [1], apart from logarithmic
corrections. We discuss implications of these results on the dependence on boundary conditions for high-dimensional percolation.
Our method is crucially based on the results in [11, 12], where the scaling was proved subject to the assumption that a suitably defined critical window contains the percolation threshold on . We also strongly rely on mean-field results for percolation on proved in [17–20]. 相似文献
12.
Vsevolod Eduardovich Adler Alexander Ivanovich Bobenko Yuri Borisovich Suris 《Letters in Mathematical Physics》2009,89(2):131-139
We consider discrete nets in Grassmannians , which generalize Q-nets (maps with planar elementary quadrilaterals) and Darboux nets (-valued maps defined on the edges of such that quadruples of points corresponding to elementary squares are all collinear). We give a geometric proof of integrability
(multidimensional consistency) of these novel nets, and show that they are analytically described by the noncommutative discrete
Darboux system.
相似文献
13.
Andrzej?Oko?ów 《Communications in Mathematical Physics》2009,289(1):335-382
A simple diffeomorphism invariant theory of connections with the non-compact structure group of real numbers is quantized. The theory is defined on a four-dimensional ‘space-time’ by an action resembling closely the
self-dual Plebański action for general relativity. The space of quantum states is constructed by means of projective techniques
by Kijowski [1]. Except for this point the applied quantization procedure is based on Loop Quantum Gravity methods. 相似文献
14.
We present the main ingredients of twistor theory leading up to and including the Penrose-Ward transform in a coordinate algebra
form which we can then ‘quantise’ by means of a functorial cocycle twist. The quantum algebras for the conformal group, twistor
space , compactified Minkowski space and the twistor correspondence space are obtained along with their canonical quantum differential calculi, both in a local
form and in a global *-algebra formulation which even in the classical commutative case provides a useful alternative to the
formulation in terms of projective varieties. We outline how the Penrose-Ward transform then quantises. As an example, we
show that the pull-back of the tautological bundle on pulls back to the basic instanton on and that this observation quantises to obtain the Connes-Landi instanton on θ-deformed S
4 as the pull-back of the tautological bundle on our θ-deformed . We likewise quantise the fibration and use it to construct the bundle on θ-deformed that maps over under the transform to the θ-deformed instanton.
The work was mainly completed while S.M. was visiting July-December 2006 at the Isaac Newton Institute, Cambridge, which both
authors thank for support. 相似文献
15.
In this paper we investigate the Schwinger parametric representation for the Feynman amplitudes of the recently discovered
renormalizable quantum field theory on the Moyal non commutative space. This representation involves new hyperbolic polynomials which are the non-commutative analogs of the usual “Kirchoff” or “Symanzik” polynomials of commutative field
theory, but contain richer topological information.
Work supported by ANR grant NT05-3-43374 “GenoPhy”. 相似文献
16.
Jonathan Weitsman 《Communications in Mathematical Physics》2008,277(1):101-125
We show how to construct measures on Banach manifolds associated to supersymmetric quantum field theories. These measures
are mathematically well-defined objects inspired by the formal path integrals appearing in the physics literature on quantum
field theory. We give three concrete examples of our construction. The first example is a family of measures on a space of functions on the two-torus, parametrized by a polynomial P (the Wess-Zumino-Landau-Ginzburg model). The second is a family of measures on a space of maps from to a Lie group (the Wess-Zumino-Novikov-Witten model). Finally we study a family of measures on the product of a space of connections on the trivial principal bundle with structure group G on a three-dimensional manifold M with a space of -valued three-forms on M.
We show that these measures are positive, and that the measures are Borel probability measures. As an application we show that formulas arising from expectations in the measures reproduce formulas discovered by Frenkel and Zhu in the theory of vertex operator algebras. We conjecture that a similar
computation for the measures , where M is a homology three-sphere, will yield the Casson invariant of M.
Dedicated to the memory of Raoul Bott
Supported in part by NSF grant DMS 04/05670. 相似文献
17.
The quantum double of the Haagerup subfactor, the first irreducible finite depth subfactor with index above 4, is the most obvious candidate for exotic modular data. We show that its modular data \({\mathcal{D}{\rm Hg}}\) fits into a family \({\mathcal{D}^\omega {\rm Hg}_{2n+1}}\) , where n ≥ 0 and \({\omega\in \mathbb{Z}_{2n+1}}\) . We show \({\mathcal{D}^0 {\rm Hg}_{2n+1}}\) is related to the subfactors Izumi hypothetically associates to the cyclic groups \({\mathbb{Z}_{2n+1}}\) . Their modular data comes equipped with canonical and dual canonical modular invariants; we compute the corresponding alpha-inductions, etc. In addition, we show there are (respectively) 1, 2, 0 subfactors of Izumi type \({\mathbb{Z}_7, \mathbb{Z}_9}\) and \({\mathbb{Z}_3^2}\) , and find numerical evidence for 2, 1, 1, 1, 2 subfactors of Izumi type \({\mathbb{Z}_{11},\mathbb{Z}_{13},\mathbb{Z}_{15},\mathbb{Z}_{17},\mathbb{Z}_{19}}\) (previously, Izumi had shown uniqueness for \({\mathbb{Z}_3}\) and \({\mathbb{Z}_5}\)), and we identify their modular data. We explain how \({\mathcal{D}{\rm Hg}}\) (more generally \({\mathcal{D}^\omega {\rm Hg}_{2n+1}}\)) is a graft of the quantum double \({\mathcal{D} Sym(3)}\) (resp. the twisted double \({\mathcal{D}^\omega D_{2n+1}}\)) by affine so(13) (resp. so\({(4n^2+4n+5)}\)) at level 2. We discuss the vertex operator algebra (or conformal field theory) realisation of the modular data \({\mathcal{D}^\omega {\rm Hg}_{2n+1}}\) . For example we show there are exactly 2 possible character vectors (giving graded dimensions of all modules) for the Haagerup VOA at central charge c = 8. It seems unlikely that any of this twisted Haagerup-Izumi modular data can be regarded as exotic, in any reasonable sense. 相似文献
18.
19.
We study the (strong-) Gibbsian character on
of the law at time t of an infinite- imensional gradient Brownian diffusion, when the initial distribution is Gibbsian 相似文献
20.
We obtain exact results in α′ for open and closed A-model topological string amplitudes on a large class of toric Calabi-Yau threefolds by using their correspondence with five
dimensional gauge theories. The toric Calabi-Yaus that we analyze are obtained as minimal resolution of cones over Y
p,q
manifolds and give rise via M-theory compactification to SU(p) gauge theories on . As an application we present a detailed study of the local case and compute open and closed genus zero Gromov-Witten invariants of the orbifold. We also display the modular structure of the topological wave function and give predictions for higher genus amplitudes.
The mirror curve in this case is the spectral curve of the relativistic A
1 Toda chain. Our results also indicate the existence of a wider class of relativistic integrable systems associated to generic
Y
p,q
geometries. 相似文献