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# MAGNETIC MONOPOLES, BOGOMOL’NYI BOUND AND SL(2, ℤ) INVARIANCE IN STRING THEORY

Modern Physics Letters A (Impact Factor: 1.11). 11/2011; 08(21). DOI: 10.1142/S0217732393001732

Source: arXiv

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**ABSTRACT:**For d=10 N=1 SUGRA coupled to d=10 N=1 SYM, anomaly cancellation places severe constraints on the allowed gauge groups. Besides the ones known to appear in string theory, only U(1)^496 and E_8 x U(1)^248 are allowed. There are no known theories of quantum gravity that reduce in some limit to these two last supergravity theories, and in this note I present some evidence that those quantum theories might not exist. The first observation is that, upon compactification, requring that the quantum theory possesses a moduli space with finite volume typically implies the existence of singularities where the 4d gauge group is enhanced, but for these two theories that gauge enhancement is problematic from the 10d point of view. I also point out that while these four supergravity theories present repulson-type singularities, the known mechanism that repairs those singularities for the first two - the non-Abelian enhancon - is not available for the last two theories. In short, these two supergravity theories might be too Abelian for their own good. Comment: 12 pages09/2008; - [Show abstract] [Hide abstract]

**ABSTRACT:**For d = 10 SUGRA coupled to d = 10 SYM, anomaly cancellation places severe constraints on the allowed gauge groups. Besides the ones known to appear in string theory, only U(1)496 and E 8 × U(1)248 are allowed. There are no known theories of quantum gravity that reduce in some limit to these two last supergravity theories, and in this note I present some evidence that those quantum theories might not exist. The first observation is that, upon compactification, requiring that the quantum theory possesses a moduli space with finite volume typically implies the existence of singularities where the 4d gauge group is enhanced, but for these two theories that gauge enhancement is problematic from the 10d point of view. I also point out that while these four supergravity theories present repulson-type singularities, the known mechanism that repairs those singularities for the first two — the non-Abelian enhan¸con — is not available for the last two theories. In short, these two supergravity theories might be too Abelian for their own good.Journal of High Energy Physics 01/2010; 2010(7):1-12. · 5.62 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**We review the properties of BPS, or supersymmetric, magnetic monopoles, with an emphasis on their low-energy dynamics and their classical and quantum bound states.After an overview of magnetic monopoles, we discuss the BPS limit and its relation to supersymmetry. We then discuss the properties and construction of multimonopole solutions with a single nontrivial Higgs field. The low-energy dynamics of these monopoles is most easily understood in terms of the moduli space and its metric. We describe in detail several known examples of these. This is then extended to cases where the unbroken gauge symmetry include a non-Abelian factor.We next turn to the generic supersymmetric Yang–Mills (SYM) case, in which several adjoint Higgs fields are present. Working first at the classical level, we describe the effects of these additional scalar fields on the monopole dynamics, and then include the contribution of the fermionic zero modes to the low-energy dynamics. The resulting low-energy effective theory is itself supersymmetric. We discuss the quantization of this theory and its quantum BPS states, which are typically composed of several loosely bound compact dyonic cores.We close with a discussion of the D-brane realization of N=4 SYM monopoles and dyons and explain the ADHMN construction of monopoles from the D-brane point of view.Physics Reports 01/2007; · 22.93 Impact Factor

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