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Magnetic monopoles are common in string models and their cosmological implications have been explored 67. As we will discuss, there are similarities and differences between D matter and magnetic monopoles.
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Magnetic monopoles are common in string models and their cosmological implications have been explored 67. As we will discuss, there are similarities and differences between D matter and magnetic monopoles.
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The disk diagram has a normalization of (Formula presented) Each open string vertex operator insertion carries a factor of (Formula presented) Hence the overall amplitude of such diagram is proportional to (Formula presented)
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The disk diagram has a normalization of (Formula presented) Each open string vertex operator insertion carries a factor of (Formula presented) Hence the overall amplitude of such diagram is proportional to (Formula presented)
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46
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0031550419
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85039594558
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Note however that some D-matter states could act as magnetic point sources of the world-volume gauge field on some higher-dimensional branes, in which case their properties are similar to that of ’t Hooft–Polyakov magnetic monopoles. For example, a D1 brane ending on two D3 branes corresponds to a magnetic monopole of the (Formula presented) gauge theory on the D3 brane world volume. This configuration is S dual to a fundamental string ending on the D3 branes. The power counting of (Formula presented) for D-matter interactions can be obtained by taking (Formula presented) of the S-dual amplitudes.
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Note however that some D-matter states could act as magnetic point sources of the world-volume gauge field on some higher-dimensional branes, in which case their properties are similar to that of ’t Hooft–Polyakov magnetic monopoles. For example, a D1 brane ending on two D3 branes corresponds to a magnetic monopole of the (Formula presented) gauge theory on the D3 brane world volume. This configuration is S dual to a fundamental string ending on the D3 branes. The power counting of (Formula presented) for D-matter interactions can be obtained by taking (Formula presented) of the S-dual amplitudes.
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55
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85039598850
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AGASA homepage, http://www.icrr.u-tokyo.ac.jp/as/as.html
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AGASA homepage, http://www.icrr.u-tokyo.ac.jp/as/as.html
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HiRes homepage, http://www.cosmic-ray.org/
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HiRes homepage, http://www.cosmic-ray.org/
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61
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For recent reviews, see S. Sarkar, hep-ph/0005256
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66
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85039590579
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D-matter states could be Bosonic or Fermionic. They correspond to the Bosonic and Fermionic zero modes of the stable D branes respectively.
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D-matter states could be Bosonic or Fermionic. They correspond to the Bosonic and Fermionic zero modes of the stable D branes respectively.
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67
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85039589590
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Notice that charge conservation with respect to the unbroken gauge group on the world volume of D matter has to be satisfied if only one end point of the open strings is attached to it. In principle, the gauge symmetry on the world volume of D matter could be broken in a realistic model so this type of requirement would not impose a restriction on the possible types of excited states.
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Notice that charge conservation with respect to the unbroken gauge group on the world volume of D matter has to be satisfied if only one end point of the open strings is attached to it. In principle, the gauge symmetry on the world volume of D matter could be broken in a realistic model so this type of requirement would not impose a restriction on the possible types of excited states.
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68
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85039600655
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At a more technical level, the zeroth mode of the Virasoro generator of an excited D-particle state is (Formula presented) Requiring (Formula presented) to annihilate the D-matter state will give us the mass formula.
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At a more technical level, the zeroth mode of the Virasoro generator of an excited D-particle state is (Formula presented) Requiring (Formula presented) to annihilate the D-matter state will give us the mass formula.
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69
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85039600574
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Whether the open string states carry momentum/winding numbers depends on whether the corresponding compact dimension is along or transverse to the world volumes of D matter and the standard model (SM) branes. If a compact dimension is along the world volumes of both the D matter and the SM branes (Neumann-Neumann boundary condition), the open string states can carry momentum but not winding numbers. Conversely, if a compact dimension is transverse to both the D matter and the SM branes (Dirichlet-Dirichlet boundary condition), the open string states can carry winding but not momentum numbers. Finally, if a compact dimension is transverse to either the D matter or the SM branes but not both (Dirichlet-Neumann boundary condition), the open string states do not carry any momentum or winding numbers.
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Whether the open string states carry momentum/winding numbers depends on whether the corresponding compact dimension is along or transverse to the world volumes of D matter and the standard model (SM) branes. If a compact dimension is along the world volumes of both the D matter and the SM branes (Neumann-Neumann boundary condition), the open string states can carry momentum but not winding numbers. Conversely, if a compact dimension is transverse to both the D matter and the SM branes (Dirichlet-Dirichlet boundary condition), the open string states can carry winding but not momentum numbers. Finally, if a compact dimension is transverse to either the D matter or the SM branes but not both (Dirichlet-Neumann boundary condition), the open string states do not carry any momentum or winding numbers.
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J. Polchinski, String Theory (Cambridge University Press, Cambridge, England, 1998).
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See, e.g., E. Witten, hep-th/0212247, and references therein.
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Witten, E.1
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