D. R. Morrison and M. R. Plesser. Summing the instantons: Quantum cohomology and mirror symmetry in toric varieties. Nuclear Phys. B, 440:279--354, 1995.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... examples for Calabi Yau manifolds is coming from Batyrev s construction using toric varieties as auxiliary device, mirror symmetry and the related quantum cohomology ( Wit91] have also been considered on toric varieties directly instead on the CalabiYau manifolds constructed from them ( Bat93] [MP95]) Kontsevich in [Kon95a] utilized the fact that toric varieties are equipped with a torus action to confirm physical calculations, as those in [CdGP91] In this spirit, starting from the original physical mirror calculations of [CdGP91] Lian, Liu 2 and Yau in [LLY97, LLY99a, LLY99b] have ....

D. R. Morrison and M. R. Plesser. Summing the instantons: Quantum cohomology and mirror symmetry in toric varieties. Nuclear Phys. B, 440:279--354, 1995.

.... recent work of Schroers [28] it is shown that in (2 1) dimensions many interesting topological solitons in the Bogomol nyi limit [8] can be studied in a unified way in terms of the gauged linear sigma models in which the Higgs potential density is given by a sum of the Fayet Iliopoulos D terms [15, 5, 34, 23]. Our study here allows us to provide an existence and uniqueness theorem for Schroers solitons. In fact, it was the general work of Schroers [28] that initiated the present unified mathematical analysis. It is hoped that the methods here are suggestive to other interesting problems in quantum ....

.... ; g = g 1 ; g 2 ; Delta Delta Delta ; g n ) with H j ; g j (j = 1; 2; Delta Delta Delta ; n) sufficiently regular (say C ff ) and M is a closed 2 surface. The scalar form (n = 1) is exactly the classical 2 dimensional conformal deformation equation for prescribed Gaussian curvature [4, 6, 18, 23, 11]. When A fails to be a symmetric positive definite matrix, there is a lack of physical motivation at this moment and our study of the system (77) is of only mathematical interest. To proceed, we will look for an analogous variational principle as in x2. Recall that, when A is nonsingular, the more ....

D. R. Morrison and M. R. Plessner, Summing the instantons: quantum cohomology and mirror symmetry in toric varieties, Nucl. Phys. B440, 279--354 (1995).

....accurate description of the singularities. Where a, b, and c are constants satisfying a 4 4 b 4 4 c 4 4 = 0. This satisfies (4.8) and gives the base of the fibration described in the last section. The structure of worldsheet instantons in the linear sigma model was analyzed in [5,21]. The instanton (4.35) has Z v (2) 12 = 2 ; Z v (1) 12 Gamma v (2) 12 = 0: 4:36) where v (A) 12 is the field strength for the worldsheet gauge group U(1)A . This means that the only fermions that can possibly have zero modes are those charged under U(1) 2 , since the spinor bundle alone ....

D. Morrison and R. Plesser, "Summing the Instantons: Quantum Cohomology and Mirror Symmetry in Toric Varieties", Nucl. Phys. B440 (1995) 279, hep-th/9412236

....to the calculation of F 1 . We do this using the general strategy described earlier. 24 We choose coordinates z 1 ; z 2 ; z 3 near the large complex structure limit, in the order dictated by our choice of the Mori cone. The discriminant has two components, which may be computed by the method of [63,64] to be Delta 1 = 1 64z 1 Gamma 768z 1 z 2 Gamma 32768z 2 1 z 2 196608z 2 1 z 2 2 4194304z 3 1 z 2 2 Gamma 16777216z 3 1 z 3 2 Gamma 294912z 2 1 z 2 2 z 3 Gamma 16777216z 3 1 z 2 2 z 3 75497472z 3 1 z 3 2 z 3 Gamma 113246208z 3 1 z 4 2 z 2 3 Delta 2 = 1 Gamma 4z ....

D. R. Morrison and M. R. Plesser, Summing the Instantons: Quantum Cohomology and Mirror Symmetry in Toric Varieties, Nucl. Phys. B440 (1995) 279--354. [hepth /9412236]

....[14,15] see also Ref. 16] and extended in Refs. 13,17] The ability to write a global version of this map and not just an asymptotic form is related to the coordinates we use on the moduli space (for a full discussion of this including a proof of Eq. 9) for a class of examples see Ref. [10]) We note that this statement of the conjecture is very reminiscent of recent results on duality in four dimensional supersymmetric gauge theories 18;19;20 . Two distinct gauge theories with nontrivial dynamics lead to the same low energy physics; further, instanton effects in one model are ....

....H is broken by c H anomalies, as desired. Note that this interaction does not break the R symmetry. However, the couplings c r have nonzero beta functions, which will cause them to grow large, so the c H gauge theory is strongly coupled at low energies. In this limit, as discussed in Refs. [8,10], this sector of the model is in a confining phase, in which the lowest component b oe of b Sigma gets a nonzero expectation value. The charged fields are then all massive, with masses of order this expectation value, and the light degrees of freedom are in the b Sigma multiplet. The ....

D. R. Morrison and M. R. Plesser, Summing the Instantons: Quantum Cohomology and Mirror Symmetry in Toric Varieties, Nucl. Phys. B440 (1995) 279--354.

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