Yang–Mills instanton sheaves with higher topological charges

Lai, Sheng-Hong; Lee, Jen-Chi; Tsai, Inn-Ho

doi:10.1142/s0219887819501123

Cited by 4 publications

(8 citation statements)

References 26 publications

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“…In a series of recent papers [12][13][14], instead of quaternion calculation for the SU (2) YM instanton, the present authors developed the biquaternion method with biconjugation operation [15] to construct SL(2, C) [16] YM instanton (or SU(2) complex YM instanton) solutions with 16k −6 moduli parameters for each k-th homotopy class. These new SL(2, C)…”

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confidence: 99%

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Sheaf lines of Yang–Mills instanton sheaves

Lai

Lee

Tsai

2019

Int. J. Geom. Methods Mod. Phys.

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We calculate a sheaf line in CP 3 which is the real line supporting sheaf points on CP 3 of SL(2, C) Yang-Mills instanton (or SU (2) complex Yang-Mills instanton) sheaves for some given ADHM data we obtained previously. We found that this sheaf line is indeed a special jumping line over S 4 spacetime. In addition, we calculate the singularity structure of the connection A and the field strength F at the corresponding singular point on S 4 of this sheaf line. We found that the order of singularity at the singular point on S 4 associated with the sheaf line in CP 3 is higher than those of other singular points associated with normal jumping lines. We conjecture that this is a general feature for sheaf lines among jumping lines. * Electronic address:

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“…Moreover, for the first time, in addition to the holomorphic vector bundles on CP 3 in the ADHM construction which have been well studied in the SU(2) instantons, the authors in [13,14] discovered and explicitly constructed the so-called YM instanton sheaves on CP 3 .…”

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Sheaf lines of Yang–Mills instanton sheaves

Lai

Lee

Tsai

2019

Int. J. Geom. Methods Mod. Phys.

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“…Recent developments of complex Yang-Mills (YM) instantons [1][2][3][4][5][6] have revealed many new mathematical structures of YM instantons which were not realized in the previous real YM instantons [7][8][9][10][11][12][13][14][15][16][17]. In particular, for the case of SU(2) complex YM instantons (or non-compact SL(2, C) [18] real YM instantons [19,20]), it was shown that for some ADHM data at some points on CP 3 the vector bundle description of 2-instanton breaks down, and one is led to use a description in terms of torsion free sheaves for these "instanton sheaves" on CP 3 [4].…”

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confidence: 99%

“…In particular, for the case of SU(2) complex YM instantons (or non-compact SL(2, C) [18] real YM instantons [19,20]), it was shown that for some ADHM data at some points on CP 3 the vector bundle description of 2-instanton breaks down, and one is led to use a description in terms of torsion free sheaves for these "instanton sheaves" on CP 3 [4]. The existence of these 2-instanton sheaves was soon extended to the complex k-instanton sheaves with higher topological charges k = 3, 4 [5].…”

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Extended complex Yang–Mills instanton sheaves

Lai¹,

Lee²,

Tsai

2020

Int. J. Geom. Methods Mod. Phys.

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In the search of YM instanton sheaves with topological charge two, the rank of β matrix in the monad construction can be dropped from the bundle case with rank β= 2 to either rank β= 1 [4] or 0 on some points of CP 3 of the sheaf cases. In this paper, we first show that the sheaf case with rank β= 0 does not exist for the previous construction of SU (2) complex YM instantons [3]. We then show that in the new "extended complex YM instantons" discovered in this paper, rank β can be either 2 on the whole CP 3 (bundle) with some given ADHM data or 1, 0 on some points of CP 3 with other ADHM data (sheaves). These extended SU (2) complex YM instantons have no real instanton counterparts. * Electronic address:

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