P. Aspinwall and D. R. Morrison, hep-th/9705104.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....9] in which the dualities are realized as classical symmetries of strings. Similarly higher dimensional critical theories (with tensionless strings) have also been constructed from this viewpoint and in particular N = 1 theories in five dimensions [10, 11, 12] and N = 1 theories in six dimensions [13, 14, 15, 16] have been engineered. In certain cases constructions can also be done using D branes in the presence of NS 5 branes [17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27] and often there is a T duality [28] which connects the two pictures (see in particular [7] An interesting duality was proposed for ....

P. Aspinwall and D. R. Morrison, hep-th/9705104.

....points of the moduli space M 4;20 . It is interesting to ask where the additional massless states come from in the dual description. The mechanism, which is nonperturbative, is that the singular points of the moduli space correspond to limits in which a two cycle on the K3 shrinks to a point. [23, 64] Type IIA 2 branes wrapped on the two cycle give 0 branes in 6d whose mass is proportional to the area of the two cycle. There is an ADE classification of the two cycles on K3 that can vanish, which has just the properties required to account for the symmetry enhancement that is obtained in the ....

P.S. Aspinwall, Phys. Lett. B357 (1995) 329, hep-th/9507012.

....see later, many more examples (with smaller values of h 1;1 ) can be produced from this one by extremal transitions. 6. 3 The Voisin Borcea examples There is a rich class of elliptic Calabi Yau threefolds studied independently by Voisin [28] and Borcea [29] and recently discussed by Aspinwall [30]. Start with a K3 surface S which admits an involution oe such that oe ( Gamma , where is the holomorphic 2 form. Build a Calabi Yau manifold of the form S Theta T 2 = oe; Gamma1) resolving singularities appropriately. These are the Voisin Borcea models. They are elliptically ....

....moduli space, while cases (iii) iv) and (v) occur at finite distance. Case (iii) includes conifold points, where Strominger [36] showed how massless solitons cure the singularity in the physics (albeit from the mirror, IIB perspective) Case (iv) corresponds to enhanced nonabelian gauge symmetry [30, 21] where a similar analysis [37] shows how the physics gets corrected nonperturbatively. Case (v) is relatively unexplored, although examples have been discussed in [38] In the conifold case [39] and in the enhanced gauge symmetry case [37] new branches of the moduli space can arise if the ....

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P.S. Aspinwall, hep-th/9510142.

....take the limit where the volume of the cylinder shrinks to zero we get a type IIB description of the same object. This is clear when we also recall that the of type IIB arose from the M theory side by compactifying on the two torus to 9 dimensions and taking the small volume limit of the torus [16, 9]. So we would say that F theory on a cylinder gives SO(32) type I heterotic strings in 10 dimensions. Note that the fact that F theory has no local on shell dynamics in the extra two dimensions make this a consistent picture [15] otherwise locality would have forced us to look for a product of ....

P.S. Aspinwall, hep-th/9508154.

....(and spacetime fermions into the F auxiliary field) scales like g Gamma3=2 . like g Gamma3 . At tree level, there are 3 bose zero modes which leads to a factor of g 3 from the zero mode integrals, which yields g Gamma3 3 = 1. At the n instanton level (an n fold cover of a line [20]) there are 2n 1 bose zero modes and we need to bring down 2n Gamma 2 factors of the four fermi interaction from the actions, yielding g Gamma3 (2n 1) Gamma(2n Gamma2) 1 as required. The counting for the singlet couplings is precisely analogous. The vertex operators in the correlation ....

P. Aspinwall and D. Morrison, Commun. Math. Phys. 151 (1993) 245, hep-th/9110048.

....volume form of K3. Thus, the 24 six dimensional gauge bosons are in a one to one correspondence with the even cohomology of K3 4 . The O(4,20) invariant metric L is the intersection form of the even cohomology of K3. We can count the number of moduli as follows. We know from mathematical work [37] that the moduli space of Ricci flat metrics for K3 is the coset O(3,19) O(3) ThetaO(19) There are also moduli associated with the antisymmetric tensor on K3, and these are obviously in a one to one correspondence with the 22 harmonic two forms on K3 (3 of them are self dual and 19 are ....

....are self dual and 19 are anti self dual) Finally we have the dilaton. It can be shown that the full moduli space is now O(4,20) O(4) ThetaO(20) the same as in the heterotic case. It takes a more delicate analysis to show that the discrete group O(4,20,Z) is also a symmetry on this moduli space [37]. To come back to our problem, we have to find non perturbative states charged under the six dimensional U(1) gauge bosons. In ten dimensions, we know of non perturbative states charged under the R R forms: they are the D branes [5] In the IIA theory the D0 brane is electrically charged under the ....

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P. Aspinwall, hep-th/9611137.

.... Geometric Engineering One of the most powerful consequences of our deeper understanding of the dynamics of string theory has been the appreciation of the fact that gauge dynamics can be encoded geoemetrically in the structure of compactifications of type II superstrings (see e.g. 1] 2] 3] 4] 5][6][7] Gauge groups arise through ADE singularities of geometry (and their fibrations [8] 9] whereas matter arises as loci of enhanced singularities [10] This not only leads to a unified description of gravitational and gauge theory dynamics, but it also leads directly to a deeper understanding ....

....parallel 7 branes coincide we get SU(n) gauge symmetry, which is encoded in the elliptic fibration acquiring an A n Gamma1 singularity. Similarly if we develop a D or E singularity we obtain SO(2n) or E n (or their modding out by outer automorphisms leading to Sp(n) SO(2n Gamma 1) F 4 , or G 2 [6][7] gauge symmetry in four dimensions. The situation can in general be more complicated: We could have a sublocus of S, consisting of a complex curve where the singularity gets enhanced. It could also happen that on a number of points on that enhanced symmetry loci, the symmetry may be further ....

P. Aspinwall and M. Gross, hep-th/9602118.

....to the requisite gauge group G with the matter content R i . As for the gauge group, given that it arises in 6 dimensions once we have ADE singularities, if we fiber that over some surface we could easily obtain ADE gauge symmetry in 4 dimensions [16] 4] 17] 18] or by using outer automorphisms [19] we can even realize non simply laced gauge groups in 4 dimensions [19] 20] In particular if we have a genus g curve with ADE singularity one expects to have ADE gauge symmetry in 4 dimensions with g adjoint hypermultiplets [17] 18] If we are interested in asymptotically free theories we would ....

.... the gauge group, given that it arises in 6 dimensions once we have ADE singularities, if we fiber that over some surface we could easily obtain ADE gauge symmetry in 4 dimensions [16] 4] 17] 18] or by using outer automorphisms [19] we can even realize non simply laced gauge groups in 4 dimensions [19][20] In particular if we have a genus g curve with ADE singularity one expects to have ADE gauge symmetry in 4 dimensions with g adjoint hypermultiplets [17] 18] If we are interested in asymptotically free theories we would want to have the genus of the curve be g 1. The case g = 1 will lead ....

P. Aspinwall and M. Gross, hep-th/9602118

.... Buscher duality [46] were thoroughfully analyzed in [47] More recently, string dualities in D = 6 have been given support by the observation that type IIA (B) with k coincident N5 brane is equivalent (Buscher T dual) to type IIB (A) around an ALE space R 4 = Gamma k [48] at vanishing B field [49]. The crucial observation is that the (non) chiral type IIB(A) admit N5 branes with N = 2; 0) respectively N = 1; 1) supersymmetry [21] For the type IIB N5 brane one expects an N = 1; 1) vector multiplet whose four scalar components are the collective coordinates for the translation of the ....

P. Aspinwall, hep-th/9508154, Nucl. Phys. Proc. Suppl. 46, 30 (1996).

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P.S. Aspinwall and J. Louis, Phys. Lett. B 369 (1996) 233, hep-th/9510234.

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