We discuss the mechanism by which adinkras holographically store the required information for the Spin(1, 3) Clifford Algebra fiber bundle in the cases of three 4D, [Formula: see text] = 1 representations: the chiral, vector and tensor supermultiplets.
We propose the recently defined "Holoraumy Tensor" to play a critical role in defining a metric to establish a correspondence between 4D, [Formula: see text]-extended 0-brane-based valise supermultiplet representations and, correspondingly via "SUSY Holography," on the space of 1D, N-extended network-based adinkras. Using an analogy with the su(3) algebra, it is argued the 0-brane holoraumy tensors play the role of the " d -coefficients" and provide a newly established tool for investigating supersymmetric representation theory.
The leading term for the energy of a bound state of k-quarks and k-antiquarks is proportional to its separation L. These k-string configurations have a Lüscher term associated with their quantum fluctuations which is typically a 1/L correction to the energy. We review the status of tensions and Lüscher terms in the context of lattice gauge theory, Hamiltonian methods, and gauge/gravity correspondence. Furthermore we explore how different representations of the k-string manifest themselves in the gauge/gravity duality. We calculate the Lüscher term for a strongly coupled SU (N ) gauge theory in (2 + 1) dimensions using the gauge/gravity correspondence. Namely, we compute one-loop corrections to a probe D4-brane embedded in the Cvetič, Gibbons, Lü, and Pope supergravity background. We investigate quantum fluctuations of both the bosonic and the fermionic sectors.
We analyze the group of maximal automorphisms of the N -extended worldline supersymmetry algebra, and its action on off-shell supermultiplets. This defines a concept of "holoraumy" that extends the notions of holonomy and curvature in a novel way and provides information about the geometry of the supermultiplet field-space. In turn, the "holoraumy" transformations of 0-brane dimensionally reduced supermultiplets provide information about Lorentz transformations in the higher-dimensional space-time from which the 0-brane supermultiplets are descended. Specifically, Spin(3) generators are encoded within 0-brane "holoraumy" tensors. Worldline supermultiplets are thus able to holographically encrypt information about higher-dimensional space-time geometry.
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