Abstract
We consider antiparallel Wilson lines in mathcal{N} = 4 super Yang-Mills in the presence of a codimension-1 defect. We compute the Wilson lines’ expectation value both at weak coupling, in the gauge theory, and at strong coupling, by finding the string configurations which are dual to this operator. These configurations display a Gross-Ooguri transition between a connected, U-shaped string phase and a phase in which the string breaks into two disconnected surfaces. We analyze in detail the critical configurations separating the two phases and compare the string result with the gauge theory one in a certain double scaling limit.
Highlights
3-dimensional hypermultiplets living on the defect, and an interaction term coupling bulk and defect degrees of freedom [11, 12]
We compute the Wilson lines’ expectation value both at weak coupling, in the gauge theory, and at strong coupling, by finding the string configurations which are dual to this operator
We analyze in detail the critical configurations separating the two phases and compare the string result with the gauge theory one in a certain double scaling limit
Summary
Supported along a pair of antiparallel lines. the path C and the scalar couplings θI can be taken, without loss of generality, to be given by xμ(α) = ∓αnμ + mμ∓ , θI = θ∓I ≡ (0, 0, sin χ∓, 0, 0, cos χ∓) ,. They determine a plane that forms an angle φ ∈ [0, π] with the direction of the defect and their symmetry axis is at a distance L > d sin φ from the defect, see figure 1 Note that both lines are contained in the same half-space, where the gauge group is the SU(N ) broken by the scalar expectation value (1.1). The free correlators of the scalar and gauge fields with mixed indices are evaluated in terms of the massive scalar propagators [14]. We limit ourselves to reporting the final contributions, which are given by rainbows on the two separate lines The (sum of the) particle-defect potentials for the two Wilson lines (labeled with a II) can instead be obtained from the remaining terms.
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