<div dir="ltr"><p class="MsoNormal" align="center" style="font-size:12.8px;text-align:center"><b><u><span lang="ES">SEMINARIOS  DEL IFLP y DEL DEPARTAMENTO</span></u></b></p><p class="MsoNormal" align="center" style="font-size:12.8px;text-align:center"><b><u>Día y horario especiales</u></b></p><p class="MsoNormal" align="center" style="font-size:12.8px;text-align:center"><b><u>LUNES 22 de MAYO – 12:30 hs</u></b></p><p class="MsoNormal" align="center" style="font-size:12.8px;text-align:center"><b><u><span lang="EN-US">AULA CHICA</span></u></b></p><p class="MsoNormal" style="font-size:12.8px;text-align:justify"><br></p><p class="MsoNormal" style="font-size:12.8px"><b><u><span lang="EN-US">TÍTULO</span></u></b><b><span lang="PT-BR">: </span></b><b><span lang="EN-US" style="font-family:"antique olive",sans-serif">"Parity anomaly in four dimensions"</span></b><span lang="PT-BR" style="background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"></span></p><p class="MsoNormal" style="font-size:12.8px;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><span lang="EN-US" style="color:rgb(69,69,69)"> </span></p><p class="MsoNormal" style="font-size:12.8px;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><b><u>EXPOSITOR:</u></b><b> </b><span class="gmail-m_-3275655119777752197gmail-m_6618327528963886864gmail-Ninguno"><b><span lang="PT-BR">Dmitry Vassilevich</span></b></span></p><p class="MsoNormal" style="font-size:12.8px;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><i><span lang="PT-BR"><font size="2">Tomsk State University & Universidade Federal do ABC</font></span></i></p><p class="MsoNormal" style="font-size:12.8px;background-image:initial;background-position:initial;background-size:initial;background-repeat:initial;background-origin:initial;background-clip:initial"><i><span lang="PT-BR"><font size="2"><br></font></span></i></p><p class="MsoNormal" style="font-size:12.8px"><b><u><span lang="EN-US">Resumen:</span></u></b><span lang="EN-US"> </span><span lang="PT-BR">It is known for more than 30 years that quantum Dirac fermions in odd dimensional spaces possess the so called parity anomaly related to the spectral asymmetry of the Dirac operator. As a result, the Chern-Simons action with the level k=1/2 is induced in 3D. We have studied Dirac fermions on four-dimensional manifolds with boundaries and demonstrated that a similar phenomenon takes place: spectral asymetry of the Dirac operator leads to a boundary Chern-Simons term. We found a somewhat unusual Chern-Simons level k=1/4, which is however consistent with the counting of boundary degrees of freedom.</span></p></div>