Integrable deformations of the Dirac--sinh-Gordon system
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866908974751678464 |
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| author | Haddad, Laith H. |
| author_facet | Haddad, Laith H. |
| contents | We construct a two-dimensional family of integrable coupled Dirac--scalar field theories in $1+1$ dimensions, parameterized by $(\thz,α)\in[0,π/2]^2$, whose Lax connection takes values in $\slC$ throughout. The family arises as the orbit of the Dirac--sinh-Gordon system under the $U(1)\times U(1)$ maximal torus of $\mathrm{Inn}(\slC)\cong PSL(2,\CC)$: the $\thz$-$U(1)$ rotates the constant phase of the Dirac mass; the $α$-$U(1)$ rotates its field-dependent phase via $β\to|β|\ee^{\imα}$. Integrability throughout the parameter space follows from a single principle: any automorphism of the Lax algebra preserves the zero-curvature condition, since the condition depends only on the Lie bracket of $\slC$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_07344 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Integrable deformations of the Dirac--sinh-Gordon system Haddad, Laith H. Mathematical Physics High Energy Physics - Theory Exactly Solvable and Integrable Systems We construct a two-dimensional family of integrable coupled Dirac--scalar field theories in $1+1$ dimensions, parameterized by $(\thz,α)\in[0,π/2]^2$, whose Lax connection takes values in $\slC$ throughout. The family arises as the orbit of the Dirac--sinh-Gordon system under the $U(1)\times U(1)$ maximal torus of $\mathrm{Inn}(\slC)\cong PSL(2,\CC)$: the $\thz$-$U(1)$ rotates the constant phase of the Dirac mass; the $α$-$U(1)$ rotates its field-dependent phase via $β\to|β|\ee^{\imα}$. Integrability throughout the parameter space follows from a single principle: any automorphism of the Lax algebra preserves the zero-curvature condition, since the condition depends only on the Lie bracket of $\slC$. |
| title | Integrable deformations of the Dirac--sinh-Gordon system |
| topic | Mathematical Physics High Energy Physics - Theory Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2603.07344 |