Effective action of β-deformed SYM theory: Farewell to two-loop BPS diagrams

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• 作者：Sergei M. Kuzenko ; Ian N. McArthur
• 关键词：QCD sum rules ; Large-me="mml40">none ; color ; black" href="/science?_ob=MathURL&_method=retrieve&_udi=B6TVC-4NN6TD9-4&_mathId=mml40&_user=10&_cdi=5531&_rdoc=3&_acct=C000050221&_version=1&_userid=10&md5=40499b6baede91dc22c0
• 刊名：Nuclear Physics B
• 出版年：2007
• 期刊代码：45_05503213
• 类别：ph
• 出版时间：27 August 2007
• 卷：778
• 期：1-2
• 页码：159-191
• 文件大小：364 K

摘要

Within the background field approach, all two-loop sunset vacuum diagrams, which occur in the Coulomb branch of me="mml2">method=retrieve&_udi=B6TVC-4NKJ0F4-3&_mathId=mml2&_user=10&_cdi=5531&_rdoc=7&_acct=C000050221&_version=1&_userid=10&md5=53fbbe58cb0336156f31897f8f699a93">mg src="http://www.sciencedirect.com/cache/MiamiImageURL/B6TVC-4NKJ0F4-3-42/0?wchp=dGLbVlb-zSkzk" alt="Click to view the MathML source" align="absbottom" border="0" height=14 width=46> superconformal theories (including me="mml3">method=retrieve&_udi=B6TVC-4NKJ0F4-3&_mathId=mml3&_user=10&_cdi=5531&_rdoc=7&_acct=C000050221&_version=1&_userid=10&md5=1fccaf0d666ebea86d856ae87250026e">mg src="http://www.sciencedirect.com/cache/MiamiImageURL/B6TVC-4NKJ0F4-3-82/0?wchp=dGLbVlb-zSkzk" alt="Click to view the MathML source" align="absbottom" border="0" height=14 width=46> SYM), obey the BPS condition me="mml4">method=retrieve&_udi=B6TVC-4NKJ0F4-3&_mathId=mml4&_user=10&_cdi=5531&_rdoc=7&_acct=C000050221&_version=1&_userid=10&md5=bd7fe195786cc447fd9e09207b881a2f" title="Click to view the MathML source">m₃=m₁+m₂, where the masses are generated by the scalars belonging to a background me="mml5">method=retrieve&_udi=B6TVC-4NKJ0F4-3&_mathId=mml5&_user=10&_cdi=5531&_rdoc=7&_acct=C000050221&_version=1&_userid=10&md5=7727f1e5beabdd1424a5b602e81b215b">mg src="http://www.sciencedirect.com/cache/MiamiImageURL/B6TVC-4NKJ0F4-3-HY/0?wchp=dGLbVlb-zSkzk" alt="Click to view the MathML source" align="absbottom" border="0" height=14 width=46> vector multiplet. These diagrams can be evaluated exactly, and prove to be homogeneous quadratic functions of the one-loop tadpoles me="mml6">method=retrieve&_udi=B6TVC-4NKJ0F4-3&_mathId=mml6&_user=10&_cdi=5531&_rdoc=7&_acct=C000050221&_version=1&_userid=10&md5=f13d1810af0aaaacf159a0a790525c21">mg src="http://www.sciencedirect.com/cache/MiamiImageURL/B6TVC-4NKJ0F4-3-NW/0?wchp=dGLbVlb-zSkzk" alt="Click to view the MathML source" align="absbottom" border="0" height=20 width=41>, me="mml7">method=retrieve&_udi=B6TVC-4NKJ0F4-3&_mathId=mml7&_user=10&_cdi=5531&_rdoc=7&_acct=C000050221&_version=1&_userid=10&md5=11e5dae537897065d2dfb97c1f300e05">mg src="http://www.sciencedirect.com/cache/MiamiImageURL/B6TVC-4NKJ0F4-3-RJ/0?wchp=dGLbVlb-zSkzk" alt="Click to view the MathML source" align="absbottom" border="0" height=20 width=41> and me="mml8">method=retrieve&_udi=B6TVC-4NKJ0F4-3&_mathId=mml8&_user=10&_cdi=5531&_rdoc=7&_acct=C000050221&_version=1&_userid=10&md5=9eb11ebfa62532949e6ebde886766e4f">mg src="http://www.sciencedirect.com/cache/MiamiImageURL/B6TVC-4NKJ0F4-3-RY/0?wchp=dGLbVlb-zSkzk" alt="Click to view the MathML source" align="absbottom" border="0" height=20 width=41>, with the coefficients being rational functions of the squared masses. We demonstrate that, if one switches on the β-deformation of the me="mml9">method=retrieve&_udi=B6TVC-4NKJ0F4-3&_mathId=mml9&_user=10&_cdi=5531&_rdoc=7&_acct=C000050221&_version=1&_userid=10&md5=7486aaac06010f423abf51c30e05abed">mg src="http://www.sciencedirect.com/cache/MiamiImageURL/B6TVC-4NKJ0F4-3-SB/0?wchp=dGLbVlb-zSkzk" alt="Click to view the MathML source" align="absbottom" border="0" height=14 width=46> SYM theory, the BPS condition no longer holds, and then generic two-loop sunset vacuum diagrams with three non-vanishing masses prove to be characterized by the following property: me="mml10">method=retrieve&_udi=B6TVC-4NKJ0F4-3&_mathId=mml10&_user=10&_cdi=5531&_rdoc=7&_acct=C000050221&_version=1&_userid=10&md5=753db0ac71180e08ccf69385c5ed8810">mg src="http://www.sciencedirect.com/cache/MiamiImageURL/B6TVC-4NKJ0F4-3-2/0?wchp=dGLbVlb-zSkzk" alt="Click to view the MathML source" align="absbottom" border="0" height=20 width=290>. In the literature, there exist several techniques to compute such diagrams. For the β-deformed me="mml11">method=retrieve&_udi=B6TVC-4NKJ0F4-3&_mathId=mml11&_user=10&_cdi=5531&_rdoc=7&_acct=C000050221&_version=1&_userid=10&md5=7393b8055aa92c5380132278e57eec6b">mg src="http://www.sciencedirect.com/cache/MiamiImageURL/B6TVC-4NKJ0F4-3-F/0?wchp=dGLbVlb-zSkzk" alt="Click to view the MathML source" align="absbottom" border="0" height=14 width=46> SYM theory, we carry out explicit two-loop calculations of the Kähler potential and me="mml12">method=retrieve&_udi=B6TVC-4NKJ0F4-3&_mathId=mml12&_user=10&_cdi=5531&_rdoc=7&_acct=C000050221&_version=1&_userid=10&md5=d4bf801014ee03dc8fd9cf0f0c58e782" title="Click to view the MathML source">F⁴ term. Our considerations are restricted to the case of β real.