| Summary: | The concepts and behaviours of k-strings and domain-walls are examined in higher representations through the scope of the Gauge-Gravity correspondence. Tensions of strings in a representation of N-ality k are examined in the strong coupling limit. Confining k-strings are discussed in four dimensional gauge theories using D5 branes in AdS5 x S5 and D3 branes in Klebanov-Strassler and Maldacena-Nunez backgrounds. Two main results are presented: The first that confining k-string tensions in N = 4 super Yang-Mills can be calculated using D5 branes in AdS5 x S5 with a cut-off in the bulk AdS. It is shown that the D5 brane can replicate a string of rank k in the antisymmetric representation. The second result shows that the S-Dual calculation to string tensions in N = 1 super Yang-Mills gravity duals reproduces the action exactly, while providing a more natural manifestation of the string charge k. Quantum broadening effects of k-string objects are investigated in both confining and non-confining theories. An old result by Luscher, Munster and Weisz is generalised to the case of a k-string. When the fundamental string is replaced by a bound state of k strings, the bound state is better described by a wrapped D-brane. The width of the k-string (the wrapped D-brane) is calculated in several confining backgrounds by using a D-brane probe and a universal result is found. The widths of k -strings in AdS5 x S5 are examined via connected world-sheet methods, and via the exchange of light supergravity modes, and are shown to disobey the confining string result. The tension of the deconfining domain walls of N = 4 Super Yang-Mills are studied at weak and strong coupling. The k-wall tension at one loop order is calculated and found to be proportional to k(N - k), the Casimir scaling. The strong coupling calculation is performed by using the Gauge-Gravity correspondence. Arguments are made that the k-wall should be identified with a 5-brane wrapping an S4 inside S5 in an AdS-Schwarzschild x S5 background. The tension at strong coupling is compared with the weak coupling result. Preliminary results for tension scaling behaviours for thermal gauge theories in two-index representations are presented and briefly discussed.
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