Tensions and Luescher terms for (2+1)-dimensional k-strings from holographic models

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 Luescher term associated with their quantum fluctuations which is typically a 1/L correction to the energy. We review the status of tensions and Luescher 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 Luescher 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 Cvetic, Gibbons, Lue, and Pope supergravity background. We investigate quantum fluctuations of both the bosonic and the fermionic sectors.