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1.
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
2.
Vincent Bouchard Albrecht Klemm Marcos Mari?o Sara Pasquetti 《Communications in Mathematical Physics》2010,296(3):589-623
We use the remodeling approach to the B-model topological string in terms of recursion relations to study open string amplitudes
at orbifold points. To this end, we clarify modular properties of the open amplitudes and rewrite them in a form that makes
their transformation properties under the modular group manifest. We exemplify this procedure for the
\mathbb C3/\mathbb Z3{{\mathbb C}^3/{\mathbb Z}_3} orbifold point of local
\mathbb P2{{\mathbb P}^2}, where we present results for topological string amplitudes for genus zero and up to three holes, and for the one-holed torus.
These amplitudes can be understood as generating functions for either open orbifold Gromov–Witten invariants of
\mathbb C3/\mathbb Z3{{\mathbb C}^3/{\mathbb Z}_3}, or correlation functions in the orbifold CFT involving insertions of both bulk and boundary operators. 相似文献
3.
4.
Michael R. Douglas Bernard Shiffman Steve Zelditch 《Communications in Mathematical Physics》2006,265(3):617-671
A fundamental problem in contemporary string/M theory is to count the number of inequivalent vacua satisfying constraints in a string theory model. This article contains the first rigorous results on the number and distribution of supersymmetric vacua of type IIb string theories compactified on a Calabi-Yau 3-fold X with flux. In particular, complete proofs of the counting formulas in Ashok-Douglas [AD] and Denef-Douglas [DD1] are given, together with van der Corput style remainder estimates.Supersymmetric vacua are critical points of certain holomorphic sections (flux superpotentials) of a line bundle
over the moduli space of complex structures on X × T
2 with respect to the Weil-Petersson connection. Flux superpotentials form a lattice of full rank in a 2 b
3(X)-dimensional real subspace
. We show that the density of critical points in
for this lattice of sections is well approximated by Gaussian measures of the kind studied in [DSZ1,DSZ2,AD,DD1].Research partially supported by DOE grant DE-FG02-96ER40959 (first author) and NSF grants DMS-0100474 (second author) and DMS-0302518 (third author). 相似文献
5.
In this paper we investigate the dynamics of relativistic (in particular, closed) strings moving in the Minkowski space
. We first derive a system with n nonlinear wave equations of Born-Infeld type which governs the motion of the string. This system can also be used to describe the extremal surfaces in
. We then show that this system enjoys some interesting geometric properties. Based on this, we give a sufficient and necessary condition for the global existence of extremal surfaces without space-like point in
with given initial data. This result corresponds to the global propagation of nonlinear waves for the system describing the motion of the string in
. We also present an explicit exact representation of the general solution for such a system. Moreover, a great deal of numerical analyses are investigated, and the numerical results show that, in phase space, various topological singularities develop in finite time in the motion of the string. Finally, some important discussions related to the theory of extremal surfaces of mixed type in
are given. 相似文献
6.
7.
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
8.
Indranil Biswas Tomás L. Gómez Norbert Hoffmann Marina Logares 《Communications in Mathematical Physics》2009,290(1):357-369
Fix integers g ≥ 3 and r ≥ 2, with r ≥ 3 if g = 3. Given a compact connected Riemann surface X of genus g, let denote the corresponding Deligne–Hitchin moduli space. We prove that the complex analytic space determines (up to an isomorphism) the unordered pair , where is the Riemann surface defined by the opposite almost complex structure on X. 相似文献
9.
10.
Gromov-Witten theory is used to define an enumerative geometry of curves in Calabi-Yau 4-folds. The main technique is to find
exact solutions to moving multiple cover integrals. The resulting invariants are analogous to the BPS counts of Gopakumar
and Vafa for Calabi-Yau 3-folds. We conjecture the 4-fold invariants to be integers and expect a sheaf theoretic explanation.
Several local Calabi-Yau 4-folds are solved exactly. Compact cases, including the sextic Calabi-Yau in , are also studied. A complete solution of the Gromov-Witten theory of the sextic is conjecturally obtained by the holomorphic
anomaly equation. 相似文献
11.
Let X be a connected Riemann surface equipped with a projective structure
. Let E be a holomorphic symplectic vector bundle over X equipped with a flat connection. There is a holomorphic symplectic structure on the total space of the pullback of E to the space of all nonzero holomorphic cotangent vectors on X. Using
, this symplectic form is quantized. A moduli space of Higgs bundles on a compact Riemann surface has a natural holomorphic symplectic structure. Using
, a quantization of this symplectic form over a Zariski open subset of the moduli space of Higgs bundles is constructed. 相似文献
12.
13.
14.
We consider a pair of isoperimetric problems arising in physics. The first concerns a Schrödinger operator in $L^2(\mathbb{R}^2)We consider a pair of isoperimetric problems arising in physics. The first concerns a Schr?dinger operator in
with an attractive interaction supported on a closed curve Γ, formally given by −Δ−αδ(x−Γ); we ask which curve of a given length maximizes the ground state energy. In the second problem we have a loop-shaped thread
Γ in
, homogeneously charged but not conducting, and we ask about the (renormalized) potential-energy minimizer. Both problems
reduce to purely geometric questions about inequalities for mean values of chords of Γ. We prove an isoperimetric theorem
for p-means of chords of curves when p ≤ 2, which implies in particular that the global extrema for the physical problems are always attained when Γ is a circle.
The letter concludes with a discussion of the p-means of chords when p > 2. 相似文献
15.
16.
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
17.
M. Bershadsky S. Cecotti H. Ooguri C. Vafa 《Communications in Mathematical Physics》1994,165(2):311-427
We develop techniques to compute higher loop string amplitudes for twistedN=2 theories with=3 (i.e. the critical case). An important ingredient is the discovery of an anomaly at every genus in decoupling of BRST trivial states, captured to all orders by a master anomaly equation. In a particular realization of theN=2 theories, the resulting string field theory is equivalent to a topological theory in six dimensions, the Kodaira-Spencer theory, which may be viewed as the closed string analog of the Chern-Simons theory. Using the mirror map this leads to computation of the number of holomorphic curves of higher genus curves in Calabi-Yau manifolds. It is shown that topological amplitudes can also be reinterpreted as computing corrections to superpotential terms appearing in the effective 4d theory resulting from compactification of standard 10d superstrings on the correspondingN=2 theory. Relations withc=1 strings are also pointed out.This article was processed by the author using the Springer-Verlag TEX CoMaPhy macro package 1991. 相似文献
18.
We describe the period matrix and other data on a higher genus Riemann surface in terms of data coming from lower genus surfaces
via an explicit sewing procedure. We consider in detail the construction of a genus two Riemann surface by either sewing two
punctured tori together or by sewing a twice-punctured torus to itself. In each case the genus two period matrix is explicitly
described as a holomorphic map from a suitable domain (parameterized by genus one moduli and sewing parameters) to the Siegel
upper half plane . Equivariance of these maps under certain subgroups of is shown. The invertibility of both maps in a particular domain of is also shown.
Support provided by the National Science Foundation DMS-0245225, and the Committee on Research at the University of California,
Santa Cruz.
Supported by The Millenium Fund, National University of Ireland, Galway. 相似文献
19.
Remodeling the B-Model 总被引:1,自引:1,他引:0
We propose a complete, new formalism to compute unambiguously B-model open and closed amplitudes in local Calabi–Yau geometries,
including the mirrors of toric manifolds. The formalism is based on the recursive solution of matrix models recently proposed
by Eynard and Orantin. The resulting amplitudes are non-perturbative in both the closed and the open moduli. The formalism
can then be used to study stringy phase transitions in the open/closed moduli space. At large radius, this formalism may be
seen as a mirror formalism to the topological vertex, but it is also valid in other phases in the moduli space. We develop
the formalism in general and provide an extensive number of checks, including a test at the orbifold point of A
p
fibrations, where the amplitudes compute the ’t Hooft expansion of vevs of Wilson loops in Chern-Simons theory on lens spaces.
We also use our formalism to predict the disk amplitude for the orbifold . 相似文献
20.
Liang Kong 《Communications in Mathematical Physics》2008,283(1):25-92
Let V be a vertex operator algebra satisfying certain reductivity and finiteness conditions such that , the category of V-modules, is a modular tensor category. We study open-closed field algebras over V equipped with nondegenerate invariant bilinear forms for both open and closed sectors. We show that they give algebras over
a certain -extension of the so-called Swiss-cheese partial dioperad, and we can obtain Ishibashi states easily in such algebras. The
Cardy condition can be formulated as an additional condition on such open-closed field algebras in terms of the action of
the modular transformation on the space of intertwining operators of V. We then derive a graphical representation of S in the modular tensor category . This result enables us to give a categorical formulation of the Cardy condition and the modular invariance condition for
1-point correlation functions on the torus. Then we incorporate these two conditions and the axioms of the open-closed field
algebra over V equipped with nondegenerate invariant bilinear forms into a tensor-categorical notion called the Cardy -algebra. In the end, we give a categorical construction of the Cardy -algebra in the Cardy case. 相似文献