Abstract
4d mathcal{N} = 1 super Yang-Mills (SYM) with simply connected gauge group G has h gapped vacua arising from the spontaneously broken discrete R-symmetry, where h is the dual Coxeter number of G. Therefore, the theory admits stable domain walls interpolating between any two vacua, but it is a nonperturbative problem to determine the low energy theory on the domain wall. We put forward an explicit answer to this question for all the domain walls for G = SU(N), Sp(N), Spin(N) and G2, and for the minimal domain wall connecting neighboring vacua for arbitrary G. We propose that the domain wall theories support specific nontrivial topological quantum field theories (TQFTs), which include the Chern-Simons theory proposed long ago by Acharya-Vafa for SU(N). We provide nontrivial evidence for our proposals by exactly matching renormalization group invariant partition functions twisted by global symmetries of SYM computed in the ultraviolet with those computed in our proposed infrared TQFTs. A crucial element in this matching is constructing the Hilbert space of spin TQFTs, that is, theories that depend on the spin structure of spacetime and admit fermionic states — a subject we delve into in some detail.
Highlights
A supersymmetric domain wall that interpolates between two arbitrary vacua a and b at x3 → ±∞ can be defined
We propose that the domain wall theories support specific nontrivial topological quantum field theories (TQFTs), which include the Chern-Simons theory proposed long ago by Acharya-Vafa for SU(N )
We provide nontrivial evidence for our proposals by exactly matching renormalization group invariant partition functions twisted by global symmetries of super Yang-Mills (SYM) computed in the ultraviolet with those computed in our proposed infrared TQFTs
Summary
Diagonalizing this permutation results on an eigenvalue gi on the fermion ψi associated to the i-th node, which is the charge of the element of the center g ∈ Γ on the i-th fundamental weight of g [36,37,38,39,40], that is gi = αg(ωi) Note that this is precisely how g ∈ Γ acts on the ultraviolet Wilson loops Wi (cf (2.7)). We can consider instead the index twisted by the Γ = Z2 one-form center symmetry, which acts on the extended Dynkin diagram as follows:. From this we learn that the folded diagram has r + 1 = N nodes, one of which has energy equal to 1, and the rest all energy equal to 2 Plugging this into (2.15) the one-form twisted partition function is. The corresponding charge is the chirality of the representation This symmetry acts by permuting the last two nodes in the unextended Dynkin diagram.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
