Towards a string bit formulation of = 4 super Yang-Mills
We show that planar = 4 Yang-Mills theory at zero 't Hooft coupling can be efficiently described in terms of 8 bosonic and 8 fermionic oscillators. We show that these oscillators can serve as world-sheet variables, the string bits, of a discretized string. There is a one to one correspondence b...
| Main Authors: | , , , |
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| Format: | Journal article |
| Language: | English |
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2006
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| _version_ | 1797078500602019840 |
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| author | Alday, L David, JR Gava, E Narain, K |
| author_facet | Alday, L David, JR Gava, E Narain, K |
| author_sort | Alday, L |
| collection | OXFORD |
| description | We show that planar = 4 Yang-Mills theory at zero 't Hooft coupling can be efficiently described in terms of 8 bosonic and 8 fermionic oscillators. We show that these oscillators can serve as world-sheet variables, the string bits, of a discretized string. There is a one to one correspondence between the on shell gauge invariant words of the free Y-M theory and the states in the oscillators' Hilbert space, obeying a local gauge and cyclicity constraints. The planar two-point functions and the three-point functions of all gauge invariant words are obtained by the simple delta-function overlap of the corresponding discrete string world sheet. At first order in the 't Hooft coupling, i.e. at one-loop in the Y-M theory, the logarithmic corrections of the planar two-point and the three-point functions can be incorporated by nearest neighbour interactions among the discretized string bits. In the SU(2) sub-sector we show that the one-loop corrections to the structure constants can be uniquely determined by the symmetries of the bit picture. For the SU(2) sub-sector we construct a gauged, linear, discrete world-sheet model for the oscillators, with only nearest neighbour couplings, which reproduces the anomalous dimension Hamiltonian up to two loops. This model also obeys BMN scaling to all loops. © SISSA 2006. |
| first_indexed | 2024-03-07T00:32:45Z |
| format | Journal article |
| id | oxford-uuid:8061d603-9d31-41e8-bd18-1117caeb28ef |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T00:32:45Z |
| publishDate | 2006 |
| record_format | dspace |
| spelling | oxford-uuid:8061d603-9d31-41e8-bd18-1117caeb28ef2022-03-26T21:22:58ZTowards a string bit formulation of = 4 super Yang-MillsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:8061d603-9d31-41e8-bd18-1117caeb28efEnglishSymplectic Elements at Oxford2006Alday, LDavid, JRGava, ENarain, KWe show that planar = 4 Yang-Mills theory at zero 't Hooft coupling can be efficiently described in terms of 8 bosonic and 8 fermionic oscillators. We show that these oscillators can serve as world-sheet variables, the string bits, of a discretized string. There is a one to one correspondence between the on shell gauge invariant words of the free Y-M theory and the states in the oscillators' Hilbert space, obeying a local gauge and cyclicity constraints. The planar two-point functions and the three-point functions of all gauge invariant words are obtained by the simple delta-function overlap of the corresponding discrete string world sheet. At first order in the 't Hooft coupling, i.e. at one-loop in the Y-M theory, the logarithmic corrections of the planar two-point and the three-point functions can be incorporated by nearest neighbour interactions among the discretized string bits. In the SU(2) sub-sector we show that the one-loop corrections to the structure constants can be uniquely determined by the symmetries of the bit picture. For the SU(2) sub-sector we construct a gauged, linear, discrete world-sheet model for the oscillators, with only nearest neighbour couplings, which reproduces the anomalous dimension Hamiltonian up to two loops. This model also obeys BMN scaling to all loops. © SISSA 2006. |
| spellingShingle | Alday, L David, JR Gava, E Narain, K Towards a string bit formulation of = 4 super Yang-Mills |
| title | Towards a string bit formulation of = 4 super Yang-Mills |
| title_full | Towards a string bit formulation of = 4 super Yang-Mills |
| title_fullStr | Towards a string bit formulation of = 4 super Yang-Mills |
| title_full_unstemmed | Towards a string bit formulation of = 4 super Yang-Mills |
| title_short | Towards a string bit formulation of = 4 super Yang-Mills |
| title_sort | towards a string bit formulation of 4 super yang mills |
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