Towards 2+4 formulation of M5-brane

Abstract

We present an attempt to formulate an action for the worldvolume theory of a single M5-brane, based on the splitting of the six worldvolume directions into 2+4, which breaks manifest Lorentz invariance from SO(1, 5) to SO(1, 1) × SO(4). To this end, an action for the free six-dimensional (2,0) chiral tensor multiplet, and separately, a nonlinearly interacting chiral 2-form action are constructed. By studying the Lagrangian formulation for the chiral 2-form with 2+4 splitting, it is suggested that, if exists, the modified diffeomorphism of the theory on curved six-dimensional space-time is less trivial than its 1+5 and 3+3 counterpart, thus hindering the coupling of the chiral 2-form to the induced metric on the worldvolume of the M5-brane. We discuss difficulties of further generalisation of the theory. Finally, in terms of Hamiltonian analysis, we show that the naively gauge-fixed failed-PST-covariantised Lagrangian has the correct number of degrees of freedom, and satisfies the hyper-surface deformation algebra.

The dual formulation of M5-brane action

“…However, we found this issue to be more nontrivial than we thought at this stage, and we will leave it as a possible future work. Similar obstacles in the PST covariantisation was also found in the 2+4 formulation [11]. We hope to report progress on these issues in the near future.…”

“…Physically, the on-shell value of the chiral 2-form part of the M5 action determines the tension of the string soliton [26]. This on-shell property of duality-symmetric action was used in [11] to obtain the nonlinearisation of the 2+4 action.…”

“…In this paper, we construct yet another alternative action. An attempt toward the 2+4 formulation of M5-brane action is put forward in [11]. However, it is still unclear whether the completion of [11] to an M5-brane is possible.…”

A covariantisation of M5-brane action in dual formulation

“…This result and the result of our paper suggests that PST covariantisation using more than 1 auxiliary scalar field is also possible. However, the paper [29] attempted to obtain a covariant M5-brane action using 2 auxiliary fields, but did not succeed.…”

5d and 6d SCFTs have no weak coupling limit

“…Since the low energy action for a single M5-brane was constructed in [6][7][8][9][10][11][12][13][14][15], it has been a longstanding goal to construct a Lorentz-invariant supersymmetric action for multiple coincident M5-branes. Despite tremendous endeavors [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31], such an action has not been successfully constructed. There are various no-go theorems excluding certain forms of the action [32][33][34][35][36][37][38][39][40][41], but whether such an action exists still remains inconclusive.…”