Polymer, composition, optical film, and liquid crystal display device

A branched polymer, comprising:

• (i) a mesogenic group-containing monomeric first component selected from the group consisting of a compound represented by General Formula (X) and a compound represented by General Formula (I),
• Qx1-Lx1-Cyx1-Lx2Cyx2-Lx3nxCyx3-Lx4-Qx2 General Formula (X)
• in the formula, QX1 and QX2 each independently represent a polymerizable group, LX1 and LX4 each independently represent a divalent linking group, LX2 and LX3 each independently represent a single bond or a divalent linking group, CyX1, CyX2, and CyX3 represent a divalent cyclic group, and nx represents an integer of 0 to 3,
• in General Formula (I), Y11, Y12 and Y13 each independently represent a methine which may be substituted or a nitrogen atom, L1, L2, and L3 each independently represent a single bond or a divalent linking group, H1, H2, and H3 each independently represent General Formula (I-A) described below or General Formula (I-B) described below, and R1, R2, and R3 each independently represent General Formula (I-R) described below,
• in General Formula (I-A), YA1 and YA2 each independently represent methine which may have a substituent or a nitrogen atom, XA represents an oxygen atom, a sulfur atom, methylene, or imino, * represents a bonding position with respect to an L1 side to an L3 side in General Formula (I) described above, and ** represents a bonding position with respect to an R1 side to a R3 side in General Formula (I) described above,
• in General Formula (I-B), YB1 and YB2 each independently represent methine which may have a substituent or a nitrogen atom, XB represents an oxygen atom, a sulfur atom, methylene, or imino, * represents a bonding position with respect to an L1 side to an L3 side in General Formula (I) described above, and ** represents a bonding position with respect to an R1 side to a R3 side in General Formula (I) described above, and
• *Lr1-Q2n1Lr2-Lr3-Q1 General Formula (I-R)
• in General Formula (I-R), * represents a bonding position with respect to an H1 side to an H3 side in General Formula (I), Lr1 represents a single bond or a divalent linking group, Q2 represents a divalent group having at least one type of cyclic structure, n1 represents an integer of 0 to 4, Lr2 and Lr3 each independently represent a divalent linking group, Q1 represents a polymerizable group or a hydrogen atom, and here, at least two of a plurality of Q1's represent a polymerizable group;
• and
• (ii) a fluorine-containing monomeric second component represented by General Formula (a) described below,
• in General Formula (a), Ra1 represents a hydrogen atom or an alkyl group having 1 to 20 carbon atoms, and Ra2 represents an alkyl group having 1 to 20 carbon atoms or an alkenyl group having 1 to 20 carbon atoms in which at least one carbon atom has a fluorine atom as a substituent.